70:@0.058194:0.966765:0.075166:0.966765:0.075166:0.950778:0.058194:0.950778:0.000000:0.000000 Descomposición en fracciones parciales:@0.404235:0.120539:0.877959:0.120539:0.877959:0.075879:0.404235:0.075879:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 M.5.1.46. Resolver aplicaciones, problemas o situaciones que pueden ser modelizados con funciones racionales, identificando las variables significativas presentes y las relaciones :@0.143622:0.931470:0.894185:0.931470:0.894185:0.921428:0.143622:0.921428:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 entre ellas, y juzgar la validez y pertinencia de los resultados obtenidos con apoyo de las TIC. :@0.143622:0.940271:0.543612:0.940271:0.543612:0.930229:0.143622:0.930229:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 M.5.1.12. Descomponer funciones racionales en fracciones parciales resolviendo los sistemas de ecuaciones correspondientes.:@0.143622:0.949072:0.683052:0.949072:0.683052:0.939030:0.143622:0.939030:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 En matemática, tiene mucho interés el estudio de funciones raciona-:@0.404235:0.153219:0.891761:0.153219:0.891761:0.136721:0.404235:0.136721:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 les. Ahora veremos cómo se aplican las propiedades algebraicas de :@0.404235:0.170570:0.895953:0.170570:0.895953:0.154072:0.404235:0.154072:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 los números reales, así como la resolución de sistemas de ecuaciones :@0.404235:0.187921:0.895986:0.187921:0.895986:0.171423:0.404235:0.171423:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 lineales para determinar fracciones parciales.:@0.404235:0.205271:0.717542:0.205271:0.717542:0.188774:0.404235:0.188774:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Ejercicio resuelto:@0.404235:0.240349:0.522213:0.240349:0.522213:0.223562:0.404235:0.223562:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Descomponer en fracciones parciales: . El denominador:@0.404235:0.274674:0.884088:0.274674:0.884088:0.258177:0.404235:0.258177:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 puede descomponerse en los factores: + 3 – 4 = ( + 4)( – 1). :@0.404235:0.299153:0.879329:0.299153:0.879329:0.282655:0.404235:0.282656:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.680803:0.299269:0.688278:0.299269:0.688278:0.282800:0.680803:0.282800:0.000000 2:@0.688273:0.292801:0.693226:0.292801:0.693226:0.283183:0.688273:0.283183:0.000000 x:@0.720815:0.299268:0.728290:0.299268:0.728290:0.282800:0.720815:0.282800:0.000000 x:@0.780614:0.299268:0.788089:0.299268:0.788089:0.282800:0.780614:0.282800:0.000000 x:@0.827583:0.299268:0.835058:0.299268:0.835058:0.282800:0.827583:0.282800:0.000000 Luego, la descomposición en fracciones parciales es::@0.404229:0.316504:0.770997:0.316504:0.770997:0.300006:0.404229:0.300006:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 = = + ; \ {–4, 1}.:@0.411954:0.344539:0.884048:0.344546:0.884048:0.328049:0.411954:0.328042:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ∀:@0.766065:0.352133:0.777637:0.352133:0.777637:0.333134:0.766065:0.333134:0.000000 x:@0.777644:0.344662:0.785119:0.344662:0.785119:0.328193:0.777644:0.328193:0.000000 :@0.789260:0.344028:0.803912:0.344028:0.803912:0.330654:0.789260:0.330654:0.000000 :@0.808054:0.343459:0.821359:0.343459:0.821359:0.330597:0.808054:0.330597:0.000000 Para obtener los valores de y , multiplicamos la igualdad por :@0.404228:0.382805:0.857859:0.382805:0.857859:0.366307:0.404228:0.366307:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A B:@0.598302:0.382920:0.634868:0.382920:0.634868:0.366452:0.598302:0.366452:0.000000:0.000000:0.000000 ( + 4)( – 1), obtenemos 7 + 3 = ( – 1) + ( + 4), donde::@0.404228:0.400156:0.842528:0.400156:0.842528:0.383658:0.404228:0.383658:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.410181:0.400271:0.417656:0.400271:0.417656:0.383802:0.410181:0.383802:0.000000 x:@0.457149:0.400271:0.464624:0.400271:0.464624:0.383802:0.457149:0.383802:0.000000 x:@0.598651:0.400271:0.606126:0.400271:0.606126:0.383802:0.598651:0.383802:0.000000 A x:@0.652805:0.400271:0.677503:0.400271:0.677503:0.383802:0.652805:0.383802:0.000000:0.000000:0.000000 B x:@0.729828:0.400271:0.752445:0.400271:0.752445:0.383802:0.729828:0.383802:0.000000:0.000000:0.000000 7 + 3 = – + + 4 ; 7 + 3 = ( + ) + (4 – ).:@0.448942:0.417506:0.847040:0.417506:0.847040:0.401009:0.448942:0.401009:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.457438:0.417622:0.464913:0.417622:0.464913:0.401153:0.457438:0.401153:0.000000 Ax A Bx:@0.511593:0.417622:0.596148:0.417622:0.596148:0.401153:0.511593:0.401153:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 B:@0.623736:0.417622:0.632926:0.417622:0.632926:0.401153:0.623736:0.401153:0.000000 x:@0.652461:0.417622:0.659936:0.417622:0.659936:0.401153:0.652461:0.401153:0.000000 x A B:@0.706615:0.417622:0.759595:0.417622:0.759595:0.401153:0.706615:0.401153:0.000000:0.000000:0.000000:0.000000:0.000000 B A:@0.799089:0.417622:0.838332:0.417622:0.838332:0.401153:0.799089:0.401153:0.000000:0.000000:0.000000 Igualamos los coeficientes y queda el sistema de ecuaciones::@0.404228:0.449186:0.829503:0.449186:0.829503:0.432688:0.404228:0.432688:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A B:@0.427963:0.479477:0.467514:0.479477:0.467514:0.463009:0.427963:0.463009:0.000000:0.000000:0.000000 + = 7:@0.439233:0.479362:0.495102:0.479362:0.495102:0.462864:0.439233:0.462864:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 – + 4 = 3:@0.427963:0.496712:0.514098:0.496712:0.514098:0.480215:0.427963:0.480215:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A:@0.438462:0.496828:0.449732:0.496828:0.449732:0.480359:0.438462:0.480359:0.000000 B:@0.477320:0.496828:0.486510:0.496828:0.486510:0.480359:0.477320:0.480359:0.000000 Por lo que la fracción original escrita en forma de fracciones parciales es::@0.404228:0.531414:0.891760:0.531414:0.891760:0.514916:0.404228:0.514916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 = + ; \ {–4, 1}.:@0.471194:0.555893:0.824800:0.555904:0.824800:0.539406:0.471194:0.539395:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ∀:@0.706815:0.563490:0.718387:0.563490:0.718387:0.544491:0.706815:0.544491:0.000000 x:@0.718396:0.556019:0.725870:0.556019:0.725870:0.539551:0.718396:0.539551:0.000000 :@0.730012:0.555385:0.744664:0.555385:0.744664:0.542012:0.730012:0.542012:0.000000 :@0.748806:0.554817:0.762111:0.554817:0.762111:0.541955:0.748806:0.541955:0.000000 Ejercicio resuelto:@0.404240:0.590981:0.522218:0.590981:0.522218:0.574194:0.404240:0.574194:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Consideremos el siguiente ejemplo. Demostrar::@0.404240:0.607956:0.737238:0.607956:0.737238:0.591458:0.404240:0.591458:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 = + – , \ {–3,1}.:@0.435449:0.642657:0.860564:0.642657:0.860564:0.626160:0.435449:0.626160:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ∀:@0.747819:0.650244:0.759392:0.650244:0.759392:0.631245:0.747819:0.631245:0.000000 s:@0.759400:0.642773:0.765777:0.642773:0.765777:0.626304:0.759400:0.626304:0.000000 :@0.769919:0.642139:0.784572:0.642139:0.784572:0.628766:0.769919:0.628766:0.000000 :@0.788714:0.641571:0.802018:0.641571:0.802018:0.628708:0.788714:0.628708:0.000000 :@0.860564:0.641689:0.865380:0.641689:0.865380:0.628242:0.860564:0.628242:0.000000 Para demostrar se puede partir del lado derecho y obtener el lado :@0.404228:0.680916:0.895948:0.680916:0.895948:0.664418:0.404228:0.664418:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 izquierdo que requiere de un procedimiento. Mientras que, partiendo :@0.404228:0.698267:0.895948:0.698267:0.895948:0.681769:0.404228:0.681769:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 del lado izquierdo, se puede obtener el lado derecho con otro tipo de :@0.404228:0.715617:0.895814:0.715617:0.895814:0.699120:0.404228:0.699120:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 procedimiento.:@0.404228:0.732968:0.512843:0.732968:0.512843:0.716470:0.404228:0.716470:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Supongamos que :@0.404228:0.767670:0.543417:0.767670:0.543417:0.751172:0.404228:0.751172:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 s:@0.532898:0.767785:0.539275:0.767785:0.539275:0.751317:0.532898:0.751317:0.000000  :@0.543284:0.767453:0.564149:0.767453:0.564149:0.752806:0.543284:0.752806:0.000000:0.000000 :@0.564014:0.766590:0.577319:0.766590:0.577319:0.753728:0.564014:0.753728:0.000000 con ≠ –3, ≠ 1. Entonces, , :@0.577319:0.767677:0.855257:0.767677:0.855257:0.751180:0.577319:0.751180:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 s:@0.612324:0.767793:0.618700:0.767793:0.618700:0.751324:0.612324:0.751324:0.000000 s:@0.663338:0.767793:0.669715:0.767793:0.669715:0.751324:0.663338:0.751324:0.000000  :@0.855141:0.767460:0.876005:0.767460:0.876005:0.752813:0.855141:0.752813:0.000000:0.000000 :@0.875709:0.766590:0.889014:0.766590:0.889014:0.753728:0.875709:0.753728:0.000000 .:@0.889014:0.767677:0.891769:0.767677:0.891769:0.751180:0.889014:0.751180:0.000000 Partimos del lado derecho y, aplicando las propiedades algebraicas de :@0.404242:0.802379:0.895839:0.802379:0.895839:0.785881:0.404242:0.785881:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 los números reales, obtenemos el siguiente desarrollo::@0.404242:0.819729:0.783492:0.819729:0.783492:0.803232:0.404242:0.803232:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 + – =:@0.404242:0.854431:0.585470:0.854431:0.585470:0.837933:0.404242:0.837933:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 = = .:@0.404242:0.896261:0.834532:0.896261:0.834532:0.879763:0.404242:0.879763:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 7 + 3:@0.696611:0.266400:0.740169:0.266400:0.740169:0.249902:0.696611:0.249902:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.705107:0.266516:0.712582:0.266516:0.712582:0.250047:0.705107:0.250047:0.000000 x:@0.681006:0.282854:0.688481:0.282854:0.688481:0.266386:0.681006:0.266386:0.000000 2:@0.688479:0.276393:0.693432:0.276393:0.693432:0.266775:0.688479:0.266775:0.000000 + 3 – 4:@0.693433:0.282745:0.755775:0.282745:0.755775:0.266247:0.693433:0.266247:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.721021:0.282861:0.728496:0.282861:0.728496:0.266392:0.721021:0.266392:0.000000 7 + 3:@0.434138:0.337072:0.477696:0.337072:0.477696:0.320574:0.434138:0.320574:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.442634:0.337187:0.450108:0.337187:0.450108:0.320719:0.442634:0.320719:0.000000 x:@0.418533:0.353526:0.426008:0.353526:0.426008:0.337057:0.418533:0.337057:0.000000 2:@0.426008:0.347064:0.430961:0.347064:0.430961:0.337446:0.426008:0.337446:0.000000 + 3 – 4:@0.430960:0.353417:0.493302:0.353417:0.493302:0.336919:0.430960:0.336919:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.458547:0.353532:0.466022:0.353532:0.466022:0.337064:0.458547:0.337064:0.000000 A:@0.654793:0.337187:0.666064:0.337187:0.666064:0.320719:0.654793:0.320719:0.000000 x:@0.642907:0.353526:0.650382:0.353526:0.650382:0.337057:0.642907:0.337057:0.000000 + 4:@0.650382:0.353410:0.677970:0.353410:0.677970:0.336913:0.650382:0.336913:0.000000:0.000000:0.000000:0.000000 B:@0.718213:0.337187:0.727402:0.337187:0.727402:0.320719:0.718213:0.320719:0.000000 x:@0.705440:0.353526:0.712915:0.353526:0.712915:0.337057:0.705440:0.337057:0.000000 – 1:@0.712915:0.353410:0.740195:0.353410:0.740195:0.336913:0.712915:0.336913:0.000000:0.000000:0.000000:0.000000 7 + 3:@0.545126:0.337072:0.588684:0.337072:0.588684:0.320574:0.545126:0.320574:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.553621:0.337187:0.561096:0.337187:0.561096:0.320719:0.553621:0.320719:0.000000 ( + 4)( – 1):@0.520100:0.353410:0.613729:0.353410:0.613729:0.336913:0.520100:0.336913:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.526053:0.353526:0.533528:0.353526:0.533528:0.337057:0.526053:0.337057:0.000000 x:@0.573022:0.353526:0.580497:0.353526:0.580497:0.337057:0.573022:0.337057:0.000000 ⇒:@0.534786:0.487160:0.552974:0.487160:0.552974:0.470218:0.534786:0.470218:0.000000 = 5, = 2.:@0.552971:0.487804:0.642400:0.487804:0.642400:0.471307:0.552971:0.471307:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A:@0.557113:0.487920:0.568383:0.487920:0.568383:0.471451:0.557113:0.471451:0.000000 B:@0.602868:0.487920:0.612057:0.487920:0.612057:0.471451:0.602868:0.471451:0.000000 7 + 3:@0.494843:0.548322:0.538402:0.548322:0.538402:0.531824:0.494843:0.531824:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.503339:0.548438:0.510814:0.548438:0.510814:0.531969:0.503339:0.531969:0.000000 x:@0.479238:0.564776:0.486713:0.564776:0.486713:0.548308:0.479238:0.548308:0.000000 2:@0.486712:0.558315:0.491665:0.558315:0.491665:0.548697:0.486712:0.548697:0.000000 + 3 – 4:@0.491665:0.564667:0.554008:0.564667:0.554008:0.548169:0.491665:0.548169:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.519253:0.564783:0.526728:0.564783:0.526728:0.548314:0.519253:0.548314:0.000000 5:@0.595569:0.548322:0.604065:0.548322:0.604065:0.531824:0.595569:0.531824:0.000000 x:@0.582295:0.564776:0.589770:0.564776:0.589770:0.548308:0.582295:0.548308:0.000000 + 4:@0.589770:0.564661:0.617358:0.564661:0.617358:0.548163:0.589770:0.548163:0.000000:0.000000:0.000000:0.000000 2:@0.660178:0.548322:0.668674:0.548322:0.668674:0.531824:0.660178:0.531824:0.000000 x:@0.647058:0.564776:0.654533:0.564776:0.654533:0.548308:0.647058:0.548308:0.000000 – 1:@0.654533:0.564661:0.681813:0.564661:0.681813:0.548163:0.654533:0.548163:0.000000:0.000000:0.000000:0.000000 s:@0.443918:0.635353:0.450294:0.635353:0.450294:0.618884:0.443918:0.618884:0.000000 2:@0.450295:0.628885:0.455248:0.628885:0.455248:0.619267:0.450295:0.619267:0.000000 + 9 + 2:@0.455249:0.635237:0.516801:0.635237:0.516801:0.618739:0.455249:0.618739:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 s:@0.482837:0.635353:0.489214:0.635353:0.489214:0.618884:0.482837:0.618884:0.000000 (s ) (s ):@0.433055:0.651691:0.527656:0.651697:0.527656:0.635229:0.433055:0.635222:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 – 1:@0.448044:0.651575:0.470218:0.651575:0.470218:0.635078:0.448044:0.635078:0.000000:0.000000:0.000000 2:@0.475657:0.645230:0.480610:0.645230:0.480610:0.635612:0.475657:0.635612:0.000000 + 3:@0.499741:0.651582:0.522223:0.651582:0.522223:0.635084:0.499741:0.635084:0.000000:0.000000:0.000000 2:@0.566363:0.635237:0.574859:0.635237:0.574859:0.618739:0.566363:0.618739:0.000000 s :@0.553782:0.651691:0.564301:0.651691:0.564301:0.635222:0.553782:0.635222:0.000000:0.000000 – 1:@0.564301:0.651575:0.587439:0.651575:0.587439:0.635078:0.564301:0.635078:0.000000:0.000000:0.000000 2:@0.417345:0.846701:0.425841:0.846701:0.425841:0.830203:0.417345:0.830203:0.000000 s :@0.404765:0.863155:0.415284:0.863155:0.415284:0.846687:0.404765:0.846687:0.000000:0.000000 – 1:@0.415284:0.863040:0.438421:0.863040:0.438421:0.846542:0.415284:0.846542:0.000000:0.000000:0.000000 1:@0.548027:0.846701:0.556523:0.846701:0.556523:0.830203:0.548027:0.830203:0.000000 s :@0.535293:0.863155:0.545812:0.863155:0.545812:0.846687:0.535293:0.846687:0.000000:0.000000 + 3:@0.545812:0.863040:0.569257:0.863040:0.569257:0.846542:0.545812:0.846542:0.000000:0.000000:0.000000 2( – 1)( + 3) + 3( + 3) – ( – 1):@0.593367:0.846701:0.831101:0.846701:0.831101:0.830203:0.593367:0.830203:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 s:@0.607816:0.846817:0.614193:0.846817:0.614193:0.830348:0.607816:0.830348:0.000000 s:@0.653379:0.846817:0.659755:0.846817:0.659755:0.830348:0.653379:0.830348:0.000000 s:@0.726837:0.846817:0.733214:0.846817:0.733214:0.830348:0.726837:0.830348:0.000000 s:@0.791491:0.846817:0.797868:0.846817:0.797868:0.830348:0.791491:0.830348:0.000000 2:@0.831096:0.840349:0.836049:0.840349:0.836049:0.830731:0.831096:0.830731:0.000000 (s :@0.664704:0.863162:0.680656:0.863162:0.680656:0.846693:0.664704:0.846693:0.000000:0.000000:0.000000 – 1) ( + 3):@0.680656:0.863046:0.764713:0.863046:0.764713:0.846548:0.680656:0.846548:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.709746:0.856694:0.714699:0.856694:0.714699:0.847076:0.709746:0.847076:0.000000 s:@0.724795:0.863162:0.731172:0.863162:0.731172:0.846693:0.724795:0.846693:0.000000 2( + 2s – 3) + 3( + 3) – ( – 2s + 1):@0.425768:0.888450:0.695193:0.888450:0.695193:0.871952:0.425768:0.871952:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 s:@0.440217:0.888565:0.446594:0.888565:0.446594:0.872097:0.440217:0.872097:0.000000 2:@0.446595:0.882097:0.451548:0.882097:0.451548:0.872479:0.446595:0.872479:0.000000 s:@0.552150:0.888565:0.558527:0.888565:0.558527:0.872097:0.552150:0.872097:0.000000 s:@0.616804:0.888565:0.623181:0.888565:0.623181:0.872097:0.616804:0.872097:0.000000 2:@0.623178:0.882097:0.628131:0.882097:0.628131:0.872479:0.623178:0.872479:0.000000 (s :@0.510477:0.904904:0.526429:0.904904:0.526429:0.888435:0.510477:0.888435:0.000000:0.000000:0.000000 – 1) ( + 3):@0.526429:0.904788:0.610485:0.904795:0.610485:0.888297:0.526429:0.888291:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.555519:0.898442:0.560472:0.898442:0.560472:0.888824:0.555519:0.888824:0.000000 s:@0.570567:0.904910:0.576944:0.904910:0.576944:0.888442:0.570567:0.888442:0.000000 s:@0.739370:0.888565:0.745746:0.888565:0.745746:0.872097:0.739370:0.872097:0.000000 2:@0.745746:0.882097:0.750699:0.882097:0.750699:0.872479:0.745746:0.872479:0.000000 + 9s + 2:@0.750699:0.888450:0.812117:0.888450:0.812117:0.871952:0.750699:0.871952:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 (s :@0.725886:0.904904:0.741837:0.904904:0.741837:0.888435:0.725886:0.888435:0.000000:0.000000:0.000000 – 1) ( + 3):@0.741779:0.904788:0.825602:0.904795:0.825602:0.888297:0.741779:0.888291:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.770809:0.898442:0.775762:0.898442:0.775762:0.888824:0.770809:0.888824:0.000000 s:@0.785800:0.904910:0.792176:0.904910:0.792176:0.888442:0.785800:0.888442:0.000000 3:@0.482944:0.846701:0.491440:0.846701:0.491440:0.830203:0.482944:0.830203:0.000000 (s :@0.462253:0.863155:0.478205:0.863155:0.478205:0.846687:0.462253:0.846687:0.000000:0.000000:0.000000 – 1):@0.478147:0.863040:0.507170:0.863040:0.507170:0.846542:0.478147:0.846542:0.000000:0.000000:0.000000:0.000000 2:@0.507170:0.856694:0.512123:0.856694:0.512123:0.847076:0.507170:0.847076:0.000000 1:@0.788325:0.760640:0.796821:0.760640:0.796821:0.744142:0.788325:0.744142:0.000000 s:@0.779887:0.777094:0.786264:0.777094:0.786264:0.760626:0.779887:0.760626:0.000000 –1:@0.786264:0.776979:0.805259:0.776979:0.805259:0.760481:0.786264:0.760481:0.000000:0.000000 1:@0.829528:0.760640:0.838024:0.760640:0.838024:0.744142:0.829528:0.744142:0.000000 s:@0.820935:0.777094:0.827312:0.777094:0.827312:0.760626:0.820935:0.760626:0.000000 +3:@0.827312:0.776979:0.846616:0.776979:0.846616:0.760481:0.827312:0.760481:0.000000:0.000000 3:@0.632000:0.635237:0.640496:0.635237:0.640496:0.618739:0.632000:0.618739:0.000000 ( – 1):@0.610982:0.651575:0.656544:0.651575:0.656544:0.635078:0.610982:0.635078:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 s :@0.616935:0.651691:0.627453:0.651691:0.627453:0.635222:0.616935:0.635222:0.000000:0.000000 2:@0.656552:0.645230:0.661506:0.645230:0.661506:0.635612:0.656552:0.635612:0.000000 1:@0.698944:0.635237:0.707440:0.635237:0.707440:0.618739:0.698944:0.618739:0.000000 s :@0.686210:0.651691:0.696729:0.651691:0.696729:0.635222:0.686210:0.635222:0.000000:0.000000 + 3:@0.696729:0.651575:0.720175:0.651575:0.720175:0.635078:0.696729:0.635078:0.000000:0.000000:0.000000 Saberes previos:@0.199646:0.108582:0.307805:0.108582:0.307805:0.093110:0.199646:0.093110:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ¿Cuáles son las pro-:@0.199884:0.137210:0.326338:0.137210:0.326338:0.122147:0.199884:0.122147:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 piedades algebraicas de los :@0.153341:0.153052:0.331137:0.153052:0.331137:0.137989:0.153341:0.137989:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 números reales? :@0.153341:0.168894:0.259934:0.168894:0.259934:0.153831:0.153341:0.153831:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Desequilibrio cognitivo:@0.199646:0.214895:0.363493:0.214895:0.363493:0.199422:0.199646:0.199422:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ¿Qué aplicaciones cono-:@0.199884:0.243522:0.358792:0.243522:0.358792:0.228459:0.199884:0.228459:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ces de las funciones racionales :@0.153341:0.259364:0.353019:0.259364:0.353019:0.244301:0.153341:0.244301:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 en problemas de electricidad?:@0.153341:0.275206:0.346249:0.275206:0.346249:0.260143:0.153341:0.260143:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Sean , :@0.199880:0.386139:0.258314:0.386139:0.258314:0.371076:0.199880:0.371076:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x y:@0.234392:0.386245:0.254533:0.386245:0.254533:0.371208:0.234392:0.371208:0.000000:0.000000:0.000000  :@0.258314:0.385941:0.277364:0.385941:0.277364:0.372568:0.258314:0.372568:0.000000:0.000000 :@0.277364:0.385136:0.289459:0.385136:0.289459:0.373444:0.277364:0.373444:0.000000 con ≠ 0, :@0.289459:0.386139:0.362616:0.386139:0.362616:0.371076:0.289459:0.371076:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.321631:0.386245:0.328456:0.386245:0.328456:0.371208:0.321631:0.371208:0.000000 y:@0.153347:0.402087:0.160366:0.402087:0.160366:0.387050:0.153347:0.387050:0.000000 ≠ 0. :@0.160366:0.401981:0.191852:0.401981:0.191852:0.386918:0.160366:0.386918:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Entonces,:@0.153347:0.424952:0.215438:0.424952:0.215438:0.409889:0.153347:0.409889:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 i.:@0.153347:0.440992:0.160295:0.440992:0.160295:0.425731:0.153347:0.425731:0.000000:0.000000 ( ) = :@0.160295:0.440794:0.225313:0.440793:0.225313:0.425730:0.160295:0.425731:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.175405:0.440900:0.182230:0.440900:0.182230:0.425863:0.175405:0.425863:0.000000 –1 –1:@0.182223:0.434992:0.207883:0.434992:0.207883:0.426210:0.182223:0.426210:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.225313:0.440898:0.232138:0.440898:0.232138:0.425862:0.225313:0.425862:0.000000 :@0.153335:0.466444:0.157117:0.466444:0.157117:0.451380:0.153335:0.451380:0.000000 x:@0.178898:0.457400:0.185723:0.457400:0.185723:0.442364:0.178898:0.442364:0.000000 y:@0.178792:0.473744:0.185811:0.473744:0.185811:0.458707:0.178792:0.458707:0.000000 –1:@0.196073:0.452787:0.206184:0.452787:0.206184:0.444005:0.196073:0.444005:0.000000:0.000000 = :@0.206183:0.466443:0.223614:0.466443:0.223614:0.451380:0.206183:0.451380:0.000000:0.000000:0.000000 y:@0.227229:0.460896:0.234247:0.460896:0.234247:0.445859:0.227229:0.445859:0.000000 x:@0.227334:0.477239:0.234159:0.477239:0.234159:0.462203:0.227334:0.462203:0.000000 ii.:@0.153351:0.502494:0.164186:0.502494:0.164186:0.487233:0.153351:0.487233:0.000000:0.000000:0.000000 ( ) = :@0.164186:0.502296:0.222396:0.502302:0.222396:0.487239:0.164186:0.487233:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 xy:@0.175408:0.502402:0.189428:0.502402:0.189428:0.487365:0.175408:0.487365:0.000000:0.000000 –1:@0.194853:0.496502:0.204964:0.496502:0.204964:0.487720:0.194853:0.487720:0.000000:0.000000 x y:@0.222396:0.502408:0.246351:0.502408:0.246351:0.487371:0.222396:0.487371:0.000000:0.000000:0.000000 –1 –1:@0.229221:0.496502:0.256461:0.496502:0.256461:0.487720:0.229221:0.487720:0.000000:0.000000:0.000000:0.000000:0.000000 .:@0.256462:0.502302:0.258977:0.502302:0.258977:0.487239:0.256462:0.487239:0.000000 Sea , :@0.153349:0.525273:0.203076:0.525273:0.203076:0.510210:0.153349:0.510210:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x y:@0.179153:0.525379:0.199294:0.525379:0.199294:0.510342:0.179153:0.510342:0.000000:0.000000:0.000000  :@0.203076:0.525075:0.222126:0.525075:0.222126:0.511702:0.203076:0.511702:0.000000:0.000000 :@0.222119:0.524269:0.234214:0.524269:0.234214:0.512576:0.222119:0.512576:0.000000 . Entonces,:@0.234214:0.525272:0.302604:0.525272:0.302604:0.510209:0.234214:0.510209:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 xy:@0.153336:0.541220:0.167355:0.541220:0.167355:0.526183:0.153336:0.526183:0.000000:0.000000 = 0 = 0 = 0.:@0.167355:0.541114:0.299890:0.541114:0.299890:0.526051:0.167355:0.526051:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ⇔:@0.196332:0.540375:0.212915:0.540375:0.212915:0.525744:0.196332:0.525744:0.000000 x:@0.216697:0.541220:0.223522:0.541220:0.223522:0.526183:0.216697:0.526183:0.000000 ∧:@0.252493:0.546971:0.261388:0.546971:0.261388:0.531427:0.252493:0.531427:0.000000 y:@0.265167:0.541220:0.272185:0.541220:0.272185:0.526183:0.265167:0.526183:0.000000 Sea un polinomio no nulo de :@0.153347:0.565867:0.359747:0.565867:0.359747:0.550804:0.153347:0.550804:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 p:@0.179152:0.565973:0.187613:0.565973:0.187613:0.550936:0.179152:0.550936:0.000000 grado ≤ 2, un polinomio de :@0.153347:0.581709:0.348102:0.581709:0.348102:0.566646:0.153347:0.566646:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 q:@0.222511:0.581815:0.230884:0.581815:0.230884:0.566778:0.222511:0.566778:0.000000 la forma ( ) = ( – )( – ), :@0.153347:0.597551:0.346521:0.597551:0.346521:0.582488:0.153347:0.582488:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 q x:@0.210374:0.597657:0.231007:0.597657:0.231007:0.582620:0.210374:0.582620:0.000000:0.000000:0.000000 x a x b:@0.259310:0.597657:0.334788:0.597657:0.334788:0.582620:0.259310:0.582620:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.153347:0.613499:0.160172:0.613499:0.160172:0.598462:0.153347:0.598462:0.000000 :@0.160172:0.613393:0.163954:0.613393:0.163954:0.598330:0.160172:0.598330:0.000000  :@0.163954:0.613195:0.183004:0.613195:0.183004:0.599822:0.163954:0.599822:0.000000:0.000000 :@0.183001:0.612390:0.195096:0.612390:0.195096:0.600697:0.183001:0.600697:0.000000 siendo , :@0.195094:0.613393:0.272314:0.613393:0.272314:0.598329:0.195094:0.598329:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a b:@0.245578:0.613498:0.268533:0.613498:0.268533:0.598461:0.245578:0.598461:0.000000:0.000000:0.000000  :@0.272314:0.613194:0.291364:0.613194:0.291364:0.599821:0.272314:0.599821:0.000000:0.000000 :@0.291364:0.612390:0.303459:0.612390:0.303459:0.600697:0.291364:0.600697:0.000000 con :@0.303459:0.613393:0.335631:0.613393:0.335631:0.598329:0.303459:0.598329:0.000000:0.000000:0.000000:0.000000:0.000000 | | + | | > 0. Entonces, la :@0.153346:0.629235:0.321293:0.629235:0.321293:0.614171:0.153346:0.614171:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.157919:0.629340:0.166116:0.629340:0.166116:0.614303:0.157919:0.614303:0.000000 b:@0.192694:0.629340:0.201155:0.629340:0.201155:0.614303:0.192694:0.614303:0.000000 función racional se :@0.153346:0.651387:0.301230:0.651400:0.301230:0.636337:0.153346:0.636324:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 p:@0.265223:0.642278:0.273684:0.642278:0.273684:0.627241:0.265223:0.627241:0.000000 q:@0.265276:0.656113:0.273649:0.656113:0.273649:0.641076:0.265276:0.641076:0.000000 descompone en fracciones :@0.153351:0.671519:0.331782:0.671519:0.331782:0.656456:0.153351:0.656456:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 parciales como::@0.153351:0.687361:0.253174:0.687361:0.253174:0.672298:0.153351:0.672298:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 p x:@0.154512:0.707519:0.175233:0.707519:0.175233:0.692482:0.154512:0.692482:0.000000:0.000000:0.000000 ( ):@0.162972:0.707413:0.180668:0.707413:0.180668:0.692350:0.162972:0.692350:0.000000:0.000000:0.000000 q x:@0.154564:0.721354:0.175197:0.721354:0.175197:0.706318:0.154564:0.706318:0.000000:0.000000:0.000000 ( ):@0.162937:0.721249:0.180633:0.721249:0.180633:0.706186:0.162937:0.706186:0.000000:0.000000:0.000000 = :@0.181846:0.713077:0.199278:0.713077:0.199278:0.698014:0.181846:0.698014:0.000000:0.000000:0.000000 A:@0.210743:0.707519:0.221033:0.707519:0.221033:0.692482:0.210743:0.692482:0.000000 x a:@0.199802:0.721354:0.231974:0.721354:0.231974:0.706318:0.199802:0.706318:0.000000:0.000000:0.000000 – :@0.206627:0.721249:0.223777:0.721249:0.223777:0.706186:0.206627:0.706186:0.000000:0.000000:0.000000 + :@0.232501:0.713077:0.249933:0.713077:0.249933:0.698014:0.232501:0.698014:0.000000:0.000000:0.000000 B:@0.262365:0.707519:0.270756:0.707519:0.270756:0.692482:0.262365:0.692482:0.000000 x b:@0.250351:0.721354:0.282787:0.721354:0.282787:0.706318:0.250351:0.706318:0.000000:0.000000:0.000000 – :@0.257176:0.721249:0.274326:0.721249:0.274326:0.706186:0.257176:0.706186:0.000000:0.000000:0.000000 , :@0.283192:0.713077:0.293271:0.713077:0.293271:0.698014:0.283192:0.698014:0.000000:0.000000:0.000000 con ≠ y ≠ .:@0.153360:0.736972:0.264142:0.736972:0.264142:0.721909:0.153360:0.721909:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x a x b:@0.181750:0.737078:0.261626:0.737078:0.261626:0.722041:0.181750:0.722041:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Siendo , constantes reales :@0.153360:0.761725:0.344118:0.761725:0.344118:0.746662:0.153360:0.746662:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A B:@0.201662:0.761831:0.226640:0.761831:0.226640:0.746794:0.201662:0.746794:0.000000:0.000000:0.000000 a determinar. Por la definición :@0.153360:0.777567:0.350614:0.777567:0.350614:0.762504:0.153360:0.762504:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 de igualdad de funciones :@0.153360:0.793409:0.319705:0.793409:0.319705:0.778346:0.153360:0.778346:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 racionales y, en consecuencia :@0.153360:0.809251:0.345422:0.809251:0.345422:0.794188:0.153360:0.794188:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 de polinomios, se obtiene un :@0.153360:0.825093:0.345967:0.825093:0.345967:0.810030:0.153360:0.810030:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 sistema de ecuaciones lineales :@0.153360:0.840935:0.351490:0.840935:0.351490:0.825872:0.153360:0.825872:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 con incógnitas , .:@0.153360:0.856777:0.279760:0.856777:0.279760:0.841714:0.153360:0.841714:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A B:@0.252267:0.856883:0.277244:0.856883:0.277244:0.841846:0.252267:0.841846:0.000000:0.000000:0.000000 Competencia :@0.199644:0.351367:0.297267:0.351367:0.297267:0.335895:0.199644:0.335895:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 matemática:@0.199644:0.363935:0.283707:0.363935:0.283707:0.348463:0.199644:0.348463:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000