96:@0.036727:0.974518:0.057230:0.974518:0.057230:0.956333:0.036727:0.956333:0.000000:0.000000
Funciones racionales y cónicas:@0.073089:0.043661:0.343993:0.043661:0.343993:0.024916:0.073089:0.024916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2.1 Adición con funciones racionales:@0.293660:0.240956:0.578985:0.240956:0.578985:0.224009:0.293660:0.224009:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sean  ,  ,  ,   polinomios reales de grado   2,   y   dos funciones racionales definidas :@0.293660:0.269746:0.930919:0.269746:0.930919:0.254034:0.293660:0.254034:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p q r s:@0.334248:0.269746:0.388218:0.269746:0.388218:0.254311:0.334248:0.254311:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
#:@0.599975:0.269192:0.615308:0.269192:0.615308:0.255476:0.599975:0.255476:0.000000
f g:@0.636919:0.269746:0.668358:0.269746:0.668358:0.254311:0.636919:0.254311:0.000000:0.000000:0.000000
como::@0.293660:0.286388:0.339439:0.286388:0.339439:0.270676:0.293660:0.270676:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.407711:0.321822:0.424591:0.321822:0.424591:0.306386:0.407711:0.306386:0.000000:0.000000:0.000000
( )   :@0.412332:0.321822:0.452533:0.321822:0.452533:0.306109:0.412332:0.306109:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.433261:0.321267:0.448594:0.321267:0.448594:0.307551:0.433261:0.307551:0.000000
p x:@0.456558:0.311965:0.478149:0.311965:0.478149:0.296530:0.456558:0.296530:0.000000:0.000000:0.000000
( ):@0.465816:0.311965:0.483027:0.311965:0.483027:0.296252:0.465816:0.296252:0.000000:0.000000:0.000000
q x:@0.455895:0.328718:0.477487:0.328718:0.477487:0.313283:0.455895:0.313283:0.000000:0.000000:0.000000
( ):@0.465154:0.328718:0.482365:0.328718:0.482365:0.313005:0.465154:0.313005:0.000000:0.000000:0.000000
,    :@0.485571:0.321827:0.504604:0.321827:0.504604:0.306114:0.485571:0.306114:0.000000:0.000000:0.000000:0.000000:0.000000
;:@0.504493:0.321272:0.516771:0.321272:0.516771:0.307556:0.504493:0.307556:0.000000
x:@0.516679:0.321827:0.524134:0.321827:0.524134:0.306391:0.516679:0.306391:0.000000
   :@0.524060:0.321827:0.547290:0.321827:0.547290:0.306114:0.524060:0.306114:0.000000:0.000000:0.000000
[:@0.528018:0.321688:0.543351:0.321688:0.543351:0.307639:0.528018:0.307639:0.000000
Dom f:@0.547217:0.321827:0.592112:0.321827:0.592112:0.306391:0.547217:0.306391:0.000000:0.000000:0.000000:0.000000:0.000000
( ),     ( ) = :@0.582614:0.321827:0.660826:0.321827:0.660826:0.306114:0.582614:0.306114:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
g x:@0.615765:0.321827:0.637210:0.321827:0.637210:0.306391:0.615765:0.306391:0.000000:0.000000:0.000000
r x:@0.664817:0.312222:0.682433:0.312222:0.682433:0.296787:0.664817:0.296787:0.000000:0.000000:0.000000
( ):@0.670100:0.312222:0.687311:0.312222:0.687311:0.296510:0.670100:0.296510:0.000000:0.000000:0.000000
s x:@0.664155:0.328975:0.682856:0.328975:0.682856:0.313540:0.664155:0.313540:0.000000:0.000000:0.000000
( ):@0.670524:0.328975:0.687734:0.328975:0.687734:0.313262:0.670524:0.313262:0.000000:0.000000:0.000000
,    :@0.693830:0.321827:0.712864:0.321827:0.712864:0.306114:0.693830:0.306114:0.000000:0.000000:0.000000:0.000000:0.000000
;:@0.712753:0.321272:0.725031:0.321272:0.725031:0.307556:0.712753:0.307556:0.000000
x:@0.724939:0.321827:0.732394:0.321827:0.732394:0.306391:0.724939:0.306391:0.000000
   :@0.732320:0.321827:0.755550:0.321827:0.755550:0.306114:0.732320:0.306114:0.000000:0.000000:0.000000
[:@0.736278:0.321688:0.751611:0.321688:0.751611:0.307639:0.736278:0.307639:0.000000
Dom g:@0.755476:0.321827:0.804937:0.321827:0.804937:0.306391:0.755476:0.306391:0.000000:0.000000:0.000000:0.000000:0.000000
( ).:@0.790874:0.321827:0.812870:0.321827:0.812870:0.306114:0.790874:0.306114:0.000000:0.000000:0.000000:0.000000
Definición. Se define la función       como sigue::@0.431398:0.350617:0.789254:0.350617:0.789254:0.334904:0.431398:0.334904:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.659538:0.350617:0.664232:0.350617:0.664232:0.335182:0.659538:0.335182:0.000000
1:@0.668116:0.350062:0.683449:0.350062:0.683449:0.336347:0.668116:0.336347:0.000000
g:@0.687314:0.350617:0.696573:0.350617:0.696573:0.335182:0.687314:0.335182:0.000000
(     )( )    ( )    ( )   :@0.367728:0.382126:0.548542:0.382126:0.548542:0.366413:0.367728:0.366413:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.372532:0.382126:0.377226:0.382126:0.377226:0.366690:0.372532:0.366690:0.000000
1:@0.381110:0.381571:0.396443:0.381571:0.396443:0.367855:0.381110:0.367855:0.000000
g x:@0.400308:0.382126:0.426539:0.382126:0.426539:0.366690:0.400308:0.366690:0.000000:0.000000:0.000000
5:@0.435209:0.381571:0.450542:0.381571:0.450542:0.367855:0.435209:0.367855:0.000000
f x:@0.454407:0.382126:0.471287:0.382126:0.471287:0.366690:0.454407:0.366690:0.000000:0.000000:0.000000
1:@0.479957:0.381571:0.495290:0.381571:0.495290:0.367855:0.479957:0.367855:0.000000
g x:@0.499155:0.382126:0.520600:0.382126:0.520600:0.366690:0.499155:0.366690:0.000000:0.000000:0.000000
5:@0.529270:0.381571:0.544603:0.381571:0.544603:0.367855:0.529270:0.367855:0.000000
p x s x  :@0.550343:0.376379:0.603705:0.376379:0.603705:0.360944:0.550343:0.360944:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( ) ( ):@0.559601:0.376379:0.600392:0.376379:0.600392:0.360666:0.559601:0.360666:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1 :@0.603705:0.375824:0.623640:0.375824:0.623640:0.362109:0.603705:0.362109:0.000000:0.000000
q x r x:@0.623640:0.376379:0.667726:0.376379:0.667726:0.360944:0.623640:0.360944:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( ) ( ):@0.632899:0.376379:0.672604:0.376379:0.672604:0.360666:0.632899:0.360666:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
q x s x:@0.584070:0.392891:0.633272:0.392891:0.633272:0.377456:0.584070:0.377456:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( )  ( ):@0.593329:0.392891:0.638150:0.392891:0.638150:0.377178:0.593329:0.377178:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
, :@0.672900:0.382124:0.680060:0.382124:0.680060:0.366412:0.672900:0.366412:0.000000:0.000000
;:@0.679971:0.381570:0.692249:0.381570:0.692249:0.367854:0.679971:0.367854:0.000000
x:@0.692157:0.382124:0.699612:0.382124:0.699612:0.366689:0.692157:0.366689:0.000000
   :@0.699538:0.382124:0.722768:0.382124:0.722768:0.366412:0.699538:0.366412:0.000000:0.000000:0.000000
[:@0.703496:0.381986:0.718829:0.381986:0.718829:0.367937:0.703496:0.367937:0.000000
Dom f:@0.722695:0.382124:0.767590:0.382124:0.767590:0.366689:0.722695:0.366689:0.000000:0.000000:0.000000:0.000000:0.000000
( )   :@0.758092:0.382124:0.795532:0.382124:0.795532:0.366412:0.758092:0.366412:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
[:@0.776260:0.381986:0.791593:0.381986:0.791593:0.367937:0.776260:0.367937:0.000000
Dom g:@0.795459:0.382124:0.844919:0.382124:0.844919:0.366689:0.795459:0.366689:0.000000:0.000000:0.000000:0.000000:0.000000
( ).:@0.830856:0.382124:0.852852:0.382124:0.852852:0.366412:0.830856:0.366412:0.000000:0.000000:0.000000:0.000000
En forma abreviada, escribimos:                  :@0.293658:0.416517:0.666134:0.416515:0.666134:0.400802:0.293658:0.400805:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.526179:0.416517:0.530873:0.416517:0.530873:0.401082:0.526179:0.401082:0.000000
1 5:@0.534757:0.415963:0.582431:0.415963:0.582431:0.402247:0.534757:0.402247:0.000000:0.000000:0.000000
g:@0.553955:0.416517:0.563214:0.416517:0.563214:0.401082:0.553955:0.401082:0.000000
p:@0.590372:0.407857:0.599631:0.407857:0.599631:0.392422:0.590372:0.392422:0.000000
q:@0.589709:0.422086:0.598968:0.422086:0.598968:0.406651:0.589709:0.406651:0.000000
1:@0.604999:0.415960:0.620332:0.415960:0.620332:0.402244:0.604999:0.402244:0.000000
r:@0.628505:0.408388:0.633788:0.408388:0.633788:0.392953:0.628505:0.392953:0.000000
s:@0.628192:0.421175:0.634561:0.421175:0.634561:0.405739:0.628192:0.405739:0.000000
5:@0.646862:0.415960:0.662195:0.415960:0.662195:0.402244:0.646862:0.402244:0.000000
ps :@0.667915:0.407883:0.686856:0.407883:0.686856:0.392447:0.667915:0.392447:0.000000:0.000000:0.000000
1 :@0.686856:0.407328:0.706791:0.407328:0.706791:0.393612:0.686856:0.393612:0.000000:0.000000
qr:@0.706791:0.407883:0.721333:0.407883:0.721333:0.392447:0.706791:0.392447:0.000000:0.000000
qs:@0.686449:0.422937:0.702077:0.422937:0.702077:0.407502:0.686449:0.407502:0.000000:0.000000
,     0,     0.:@0.724279:0.416515:0.821212:0.416515:0.821212:0.400802:0.724279:0.400802:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
q:@0.731348:0.416515:0.740607:0.416515:0.740607:0.401080:0.731348:0.401080:0.000000
?:@0.744491:0.417056:0.759824:0.417056:0.759824:0.401884:0.744491:0.401884:0.000000
s:@0.779648:0.416515:0.786017:0.416515:0.786017:0.401080:0.779648:0.401080:0.000000
?:@0.789901:0.417056:0.805235:0.417056:0.805235:0.401884:0.789901:0.401884:0.000000
Las imágenes de funciones racionales son números reales, por lo tanto, las operaciones :@0.293642:0.445305:0.931324:0.445305:0.931324:0.429593:0.293642:0.429593:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
con funciones racionales heredan las propiedades algebraicas de los números reales. :@0.293642:0.461947:0.910583:0.461947:0.910583:0.446234:0.293642:0.446234:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Dadas las funciones racionales  ,  , la función       está definida únicamente en el :@0.293642:0.490737:0.930938:0.490737:0.930938:0.475025:0.293642:0.475025:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f g:@0.530893:0.490737:0.553920:0.490737:0.553920:0.475302:0.530893:0.475302:0.000000:0.000000:0.000000
f:@0.644153:0.490737:0.648846:0.490737:0.648846:0.475302:0.644153:0.475302:0.000000
1:@0.654534:0.490183:0.669868:0.490183:0.669868:0.476467:0.654534:0.476467:0.000000
g:@0.675611:0.490737:0.684869:0.490737:0.684869:0.475302:0.675611:0.475302:0.000000
conjunto :@0.293623:0.507379:0.363876:0.507379:0.363876:0.491667:0.293623:0.491667:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Dom f:@0.363755:0.507379:0.408650:0.507379:0.408650:0.491944:0.363755:0.491944:0.000000:0.000000:0.000000:0.000000:0.000000
( )   :@0.399152:0.507379:0.436592:0.507379:0.436592:0.491667:0.399152:0.491667:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
>:@0.417320:0.507241:0.432653:0.507241:0.432653:0.493192:0.417320:0.493192:0.000000
Dom g:@0.436519:0.507379:0.485979:0.507379:0.485979:0.491944:0.436519:0.491944:0.000000:0.000000:0.000000:0.000000:0.000000
( ).:@0.471916:0.507379:0.493913:0.507379:0.493913:0.491667:0.471916:0.491667:0.000000:0.000000:0.000000:0.000000
Ejercicio resuelto:@0.293623:0.536170:0.422205:0.536170:0.422205:0.519500:0.293623:0.519500:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Consideremos las funciones racionales  ,  , definidas como sigue::@0.293623:0.564960:0.763524:0.564960:0.763524:0.549247:0.293623:0.549247:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f g:@0.576911:0.564960:0.597858:0.564960:0.597858:0.549525:0.576911:0.549525:0.000000:0.000000:0.000000
 :@0.449752:0.595921:0.453628:0.595921:0.453628:0.580812:0.449752:0.580812:0.000000
f x:@0.507680:0.595921:0.523911:0.595921:0.523911:0.581078:0.507680:0.581078:0.000000:0.000000:0.000000
( )           ,   :@0.512122:0.595921:0.595649:0.595921:0.595649:0.580812:0.512122:0.580812:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.532247:0.595707:0.546991:0.595707:0.546991:0.582519:0.532247:0.582519:0.000000
;:@0.595490:0.595707:0.607296:0.595707:0.607296:0.582519:0.595490:0.582519:0.000000
x:@0.607207:0.595921:0.614376:0.595921:0.614376:0.581078:0.607207:0.581078:0.000000
     \ {1},:@0.614305:0.595921:0.683849:0.595921:0.683849:0.580812:0.614305:0.580812:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.618110:0.596094:0.632855:0.596094:0.632855:0.582585:0.618110:0.582585:0.000000
:@0.636572:0.595347:0.649351:0.595347:0.649351:0.582945:0.636572:0.582945:0.000000
 :@0.449752:0.622234:0.453628:0.622234:0.453628:0.607125:0.449752:0.607125:0.000000
g:@0.507680:0.622234:0.516583:0.622234:0.516583:0.607391:0.507680:0.607391:0.000000
(x)            ,   :@0.516512:0.622234:0.604269:0.622234:0.604269:0.607125:0.516512:0.607125:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.537062:0.622020:0.551806:0.622020:0.551806:0.608832:0.537062:0.608832:0.000000
;:@0.604110:0.622020:0.615916:0.622020:0.615916:0.608832:0.604110:0.608832:0.000000
x:@0.615827:0.622234:0.622996:0.622234:0.622996:0.607391:0.615827:0.607391:0.000000
     \ { 1, 1}.:@0.622925:0.622234:0.722466:0.622234:0.722466:0.607125:0.622925:0.607125:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.626730:0.622407:0.641475:0.622407:0.641475:0.608898:0.626730:0.608898:0.000000
:@0.645191:0.621660:0.657971:0.621660:0.657971:0.609258:0.645191:0.609258:0.000000
2:@0.676167:0.622020:0.690911:0.622020:0.690911:0.608832:0.676167:0.608832:0.000000
2 :@0.562015:0.589575:0.574529:0.589575:0.574529:0.574466:0.562015:0.574466:0.000000:0.000000
x:@0.550344:0.601207:0.557513:0.601207:0.557513:0.586365:0.550344:0.586365:0.000000
2:@0.557513:0.600834:0.572257:0.600834:0.572257:0.587645:0.557513:0.587645:0.000000
1 :@0.572257:0.601207:0.584771:0.601207:0.584771:0.586098:0.572257:0.586098:0.000000:0.000000
2 :@0.565726:0.615809:0.578240:0.615809:0.578240:0.600700:0.565726:0.600700:0.000000:0.000000
x:@0.554056:0.627448:0.561224:0.627448:0.561224:0.612606:0.554056:0.612606:0.000000
 1 :@0.561224:0.627448:0.593545:0.627448:0.593545:0.612339:0.561224:0.612339:0.000000:0.000000:0.000000:0.000000
2:@0.566287:0.627075:0.581031:0.627075:0.581031:0.613886:0.566287:0.613886:0.000000
5:@0.500927:0.625710:0.505214:0.625710:0.505214:0.574743:0.500927:0.574743:0.000000
De la definición de las funciones racionales  ,  , se tiene:  :@0.293660:0.659937:0.703804:0.659937:0.703804:0.644224:0.293660:0.644224:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f g:@0.608086:0.659937:0.629034:0.659937:0.629034:0.644502:0.608086:0.644502:0.000000:0.000000:0.000000
Dom f:@0.293635:0.688727:0.338954:0.688727:0.338954:0.673292:0.293635:0.673292:0.000000:0.000000:0.000000:0.000000:0.000000
( )     \ {1}, :@0.329341:0.688727:0.423903:0.688727:0.423903:0.673015:0.329341:0.673015:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.348581:0.688173:0.363914:0.688173:0.363914:0.674457:0.348581:0.674457:0.000000
R:@0.368645:0.687868:0.381935:0.687868:0.381935:0.674970:0.368645:0.674970:0.000000
Dom g:@0.424584:0.688727:0.474468:0.688727:0.474468:0.673292:0.424584:0.673292:0.000000:0.000000:0.000000:0.000000:0.000000
( )     \ {–1, 1}. Entonces,       es la función racional definida :@0.460291:0.688727:0.930839:0.688727:0.930839:0.673015:0.460291:0.673015:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.484095:0.688173:0.499428:0.688173:0.499428:0.674457:0.484095:0.674457:0.000000
R:@0.504159:0.687868:0.517449:0.687868:0.517449:0.674970:0.504159:0.674970:0.000000
f:@0.662019:0.688727:0.666713:0.688727:0.666713:0.673292:0.662019:0.673292:0.000000
1:@0.671425:0.688173:0.686759:0.688173:0.686759:0.674457:0.671425:0.674457:0.000000
g:@0.691489:0.688727:0.700748:0.688727:0.700748:0.673292:0.691489:0.673292:0.000000
como::@0.293672:0.705369:0.339451:0.705369:0.339451:0.689657:0.293672:0.689657:0.000000:0.000000:0.000000:0.000000:0.000000
(     )( )    ( )    ( ) :@0.293672:0.736767:0.455306:0.736767:0.455306:0.721054:0.293672:0.721054:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.298476:0.736767:0.303170:0.736767:0.303170:0.721331:0.298476:0.721331:0.000000
1:@0.307054:0.736212:0.322387:0.736212:0.322387:0.722496:0.307054:0.722496:0.000000
g x:@0.326253:0.736767:0.352483:0.736767:0.352483:0.721331:0.326253:0.721331:0.000000:0.000000:0.000000
5:@0.361153:0.736212:0.376486:0.736212:0.376486:0.722496:0.361153:0.722496:0.000000
f x:@0.380352:0.736767:0.397231:0.736767:0.397231:0.721331:0.380352:0.721331:0.000000:0.000000:0.000000
1:@0.405901:0.736212:0.421234:0.736212:0.421234:0.722496:0.405901:0.722496:0.000000
g x:@0.425100:0.736767:0.446544:0.736767:0.446544:0.721331:0.425100:0.721331:0.000000:0.000000:0.000000
5:@0.455214:0.736212:0.470547:0.736212:0.470547:0.722496:0.455214:0.722496:0.000000
2 :@0.484535:0.730776:0.497549:0.730776:0.497549:0.715063:0.484535:0.715063:0.000000:0.000000
x:@0.472401:0.742875:0.479856:0.742875:0.479856:0.727440:0.472401:0.727440:0.000000
2:@0.479856:0.742487:0.495189:0.742487:0.495189:0.728771:0.479856:0.728771:0.000000
1 :@0.495189:0.742875:0.508203:0.742875:0.508203:0.727162:0.495189:0.727162:0.000000:0.000000
1 :@0.503568:0.736221:0.523411:0.736221:0.523411:0.722505:0.503568:0.722505:0.000000:0.000000
x:@0.537645:0.731928:0.545100:0.731928:0.545100:0.716493:0.537645:0.716493:0.000000
x:@0.523888:0.743916:0.531343:0.743916:0.531343:0.728481:0.523888:0.728481:0.000000
 1 :@0.531343:0.743916:0.564955:0.743916:0.564955:0.728204:0.531343:0.728204:0.000000:0.000000:0.000000:0.000000
2:@0.536607:0.743528:0.551941:0.743528:0.551941:0.729813:0.536607:0.729813:0.000000
 :@0.293660:0.769416:0.297691:0.769416:0.297691:0.753704:0.293660:0.753704:0.000000
5:@0.363942:0.768862:0.379276:0.768862:0.379276:0.755146:0.363942:0.755146:0.000000
 :@0.379184:0.769416:0.383215:0.769416:0.383215:0.753704:0.379184:0.753704:0.000000
2 :@0.397208:0.764982:0.410222:0.764982:0.410222:0.749270:0.397208:0.749270:0.000000:0.000000
x:@0.385074:0.777080:0.392529:0.777080:0.392529:0.761645:0.385074:0.761645:0.000000
2:@0.392529:0.776692:0.407862:0.776692:0.407862:0.762976:0.392529:0.762976:0.000000
1  (:@0.407862:0.777080:0.441849:0.776421:0.441849:0.760708:0.407862:0.761368:0.000000:0.000000:0.000000:0.000000
 + :@0.416241:0.769416:0.435127:0.769416:0.435127:0.753704:0.416241:0.753704:0.000000:0.000000:0.000000
x:@0.477170:0.762978:0.484625:0.762978:0.484625:0.747542:0.477170:0.747542:0.000000
 :@0.484625:0.762978:0.488657:0.762978:0.488657:0.747265:0.484625:0.747265:0.000000
x:@0.441849:0.776421:0.449303:0.776421:0.449303:0.760986:0.441849:0.760986:0.000000
2:@0.449303:0.776033:0.464637:0.776033:0.464637:0.762317:0.449303:0.762317:0.000000
1) (:@0.464637:0.776421:0.487407:0.776421:0.487407:0.760708:0.464637:0.760708:0.000000:0.000000:0.000000:0.000000
x:@0.487407:0.776421:0.494861:0.776421:0.494861:0.760986:0.487407:0.760986:0.000000
1:@0.494861:0.776033:0.510195:0.776033:0.510195:0.762317:0.494861:0.762317:0.000000
1) :@0.510195:0.776421:0.528087:0.776421:0.528087:0.760708:0.510195:0.760708:0.000000:0.000000:0.000000
   :@0.523880:0.769416:0.547101:0.769416:0.547101:0.753704:0.523880:0.753704:0.000000:0.000000:0.000000
5:@0.527829:0.768862:0.543162:0.768862:0.543162:0.755146:0.527829:0.755146:0.000000
2(   1) :@0.548960:0.762352:0.612797:0.762352:0.612797:0.746640:0.548960:0.746640:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.562821:0.762352:0.570276:0.762352:0.570276:0.746917:0.562821:0.746917:0.000000
2 1 :@0.579572:0.761964:0.632732:0.761964:0.632732:0.748248:0.579572:0.748248:0.000000:0.000000:0.000000:0.000000
x x:@0.632732:0.762352:0.652520:0.762352:0.652520:0.746917:0.632732:0.746917:0.000000:0.000000:0.000000
(:@0.640187:0.762352:0.645065:0.762352:0.645065:0.746640:0.640187:0.746640:0.000000
2:@0.652520:0.761964:0.667853:0.761964:0.667853:0.748248:0.652520:0.748248:0.000000
1) :@0.667853:0.762352:0.685745:0.762352:0.685745:0.746640:0.667853:0.746640:0.000000:0.000000:0.000000
(:@0.575547:0.776901:0.580425:0.776901:0.580425:0.761189:0.575547:0.761189:0.000000
x:@0.580425:0.776901:0.587880:0.776901:0.587880:0.761466:0.580425:0.761466:0.000000
2:@0.587880:0.776513:0.603213:0.776513:0.603213:0.762797:0.587880:0.762797:0.000000
1) (:@0.603213:0.776901:0.625983:0.776901:0.625983:0.761189:0.603213:0.761189:0.000000:0.000000:0.000000:0.000000
x:@0.625983:0.776901:0.633438:0.776901:0.633438:0.761466:0.625983:0.761466:0.000000
1:@0.633438:0.776513:0.648771:0.776513:0.648771:0.762797:0.633438:0.762797:0.000000
1) :@0.648771:0.776901:0.666663:0.776901:0.666663:0.761189:0.648771:0.761189:0.000000:0.000000:0.000000
 :@0.293660:0.803400:0.297691:0.803400:0.297691:0.787687:0.293660:0.787687:0.000000
5:@0.363942:0.802845:0.379276:0.802845:0.379276:0.789129:0.363942:0.789129:0.000000
 :@0.379184:0.803400:0.383215:0.803400:0.383215:0.787687:0.379184:0.787687:0.000000
2   2 :@0.385072:0.794994:0.439153:0.794994:0.439153:0.779282:0.385072:0.779282:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.394055:0.794994:0.401510:0.794994:0.401510:0.779559:0.394055:0.779559:0.000000
2 1  2:@0.410806:0.794606:0.487140:0.794606:0.487140:0.780890:0.410806:0.780890:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.459088:0.794994:0.466543:0.794994:0.466543:0.779559:0.459088:0.779559:0.000000
:@0.466543:0.794994:0.471807:0.794994:0.471807:0.779282:0.466543:0.779282:0.000000
x:@0.487140:0.794994:0.494595:0.794994:0.494595:0.779559:0.487140:0.779559:0.000000
 :@0.494595:0.794994:0.498627:0.794994:0.498627:0.779282:0.494595:0.779282:0.000000
(:@0.398262:0.809543:0.403140:0.809543:0.403140:0.793831:0.398262:0.793831:0.000000
x:@0.403140:0.809543:0.410595:0.809543:0.410595:0.794108:0.403140:0.794108:0.000000
2:@0.410595:0.809155:0.425928:0.809155:0.425928:0.795439:0.410595:0.795439:0.000000
1) (:@0.425928:0.809543:0.448698:0.809543:0.448698:0.793831:0.425928:0.793831:0.000000:0.000000:0.000000:0.000000
x:@0.448698:0.809543:0.456153:0.809543:0.456153:0.794108:0.448698:0.794108:0.000000
1:@0.456153:0.809155:0.471486:0.809155:0.471486:0.795439:0.456153:0.795439:0.000000
1) :@0.471486:0.809543:0.489378:0.809543:0.489378:0.793831:0.471486:0.793831:0.000000:0.000000:0.000000
 :@0.498934:0.803400:0.502966:0.803400:0.502966:0.787687:0.498934:0.787687:0.000000
5 :@0.502885:0.802845:0.522728:0.802845:0.522728:0.789129:0.502885:0.789129:0.000000:0.000000
3  :@0.530459:0.796633:0.556193:0.796633:0.556193:0.780921:0.530459:0.780921:0.000000:0.000000:0.000000:0.000000
x:@0.539442:0.796633:0.546897:0.796633:0.546897:0.781198:0.539442:0.781198:0.000000
2 2:@0.556193:0.796245:0.594314:0.796245:0.594314:0.782529:0.556193:0.782529:0.000000:0.000000:0.000000
x:@0.571526:0.796633:0.578981:0.796633:0.578981:0.781198:0.571526:0.781198:0.000000
2 :@0.594314:0.796633:0.607328:0.796633:0.607328:0.780921:0.594314:0.780921:0.000000:0.000000
(:@0.523645:0.811182:0.528523:0.811182:0.528523:0.795470:0.523645:0.795470:0.000000
x:@0.528523:0.811182:0.535978:0.811182:0.535978:0.795747:0.528523:0.795747:0.000000
2:@0.535978:0.810794:0.551311:0.810794:0.551311:0.797078:0.535978:0.797078:0.000000
1) (:@0.551311:0.811182:0.574081:0.811182:0.574081:0.795470:0.551311:0.795470:0.000000:0.000000:0.000000:0.000000
x:@0.574081:0.811182:0.581536:0.811182:0.581536:0.795747:0.574081:0.795747:0.000000
1:@0.581536:0.810794:0.596869:0.810794:0.596869:0.797078:0.581536:0.797078:0.000000
1) :@0.596869:0.811182:0.614761:0.811182:0.614761:0.795470:0.596869:0.795470:0.000000:0.000000:0.000000
   :@0.611483:0.803400:0.634706:0.803400:0.634706:0.787687:0.611483:0.787687:0.000000:0.000000:0.000000
5:@0.615434:0.802845:0.630767:0.802845:0.630767:0.789129:0.615434:0.789129:0.000000
(:@0.640655:0.811165:0.645533:0.811165:0.645533:0.795452:0.640655:0.795452:0.000000
x:@0.645533:0.811165:0.652988:0.811165:0.652988:0.795729:0.645533:0.795729:0.000000
2:@0.652988:0.810776:0.668321:0.810776:0.668321:0.797061:0.652988:0.797061:0.000000
1) (:@0.668321:0.811165:0.691091:0.811165:0.691091:0.795452:0.668321:0.795452:0.000000:0.000000:0.000000:0.000000
x:@0.691091:0.811165:0.698546:0.811165:0.698546:0.795729:0.691091:0.795729:0.000000
1:@0.698546:0.810776:0.713879:0.810776:0.713879:0.797061:0.698546:0.797061:0.000000
1) :@0.713879:0.811165:0.731771:0.811165:0.731771:0.795452:0.713879:0.795452:0.000000:0.000000:0.000000
(:@0.636109:0.795826:0.640987:0.795826:0.640987:0.780114:0.636109:0.780114:0.000000
x:@0.640987:0.795826:0.648442:0.795826:0.648442:0.780391:0.640987:0.780391:0.000000
2:@0.648442:0.795438:0.663775:0.795438:0.663775:0.781722:0.648442:0.781722:0.000000
1) (3:@0.663775:0.795826:0.695527:0.795826:0.695527:0.780114:0.663775:0.780114:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.695527:0.795826:0.702982:0.795826:0.702982:0.780391:0.695527:0.780391:0.000000
1:@0.702982:0.795438:0.718315:0.795438:0.718315:0.781722:0.702982:0.781722:0.000000
2) :@0.718315:0.795826:0.736207:0.795826:0.736207:0.780114:0.718315:0.780114:0.000000:0.000000:0.000000
 :@0.293660:0.834904:0.297691:0.834904:0.297691:0.819192:0.293660:0.819192:0.000000
5:@0.363942:0.834350:0.379276:0.834350:0.379276:0.820634:0.363942:0.820634:0.000000
 :@0.379184:0.834904:0.383215:0.834904:0.383215:0.819192:0.379184:0.819192:0.000000
3   2 :@0.385089:0.828976:0.433905:0.828976:0.433905:0.813264:0.385089:0.813264:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.394072:0.828976:0.401527:0.828976:0.401527:0.813541:0.394072:0.813541:0.000000
1:@0.405558:0.828588:0.420891:0.828588:0.420891:0.814872:0.405558:0.814872:0.000000
(:@0.388360:0.843525:0.393238:0.843525:0.393238:0.827813:0.388360:0.827813:0.000000
x:@0.393238:0.843525:0.400693:0.843525:0.400693:0.828090:0.393238:0.828090:0.000000
1:@0.400693:0.843137:0.416027:0.843137:0.416027:0.829421:0.400693:0.829421:0.000000
1) :@0.416027:0.843525:0.433918:0.843525:0.433918:0.827813:0.416027:0.827813:0.000000:0.000000:0.000000
   3   :@0.436594:0.834904:0.491863:0.834904:0.491863:0.819192:0.436594:0.819192:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5 2:@0.440543:0.834350:0.487924:0.834350:0.487924:0.820634:0.440543:0.820634:0.000000:0.000000:0.000000
1:@0.504273:0.829861:0.513255:0.829861:0.513255:0.814149:0.504273:0.814149:0.000000
x:@0.493083:0.841849:0.500538:0.841849:0.500538:0.825443:0.493083:0.825443:0.000000
1:@0.500538:0.841460:0.515871:0.841460:0.515871:0.827745:0.500538:0.827745:0.000000
1 :@0.515871:0.841849:0.528885:0.841849:0.528885:0.826136:0.515871:0.826136:0.000000:0.000000
 :@0.523684:0.834904:0.527715:0.834904:0.527715:0.819192:0.523684:0.819192:0.000000
Esta función tiene dos asíntotas: una horizontal definida como     {( , 3) |      } y una :@0.293660:0.863697:0.930990:0.863697:0.930990:0.847985:0.293660:0.847985:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.747031:0.863697:0.756915:0.863697:0.756915:0.848262:0.747031:0.848262:0.000000
h:@0.756854:0.866870:0.762391:0.866870:0.762391:0.857871:0.756854:0.857871:0.000000
5:@0.766273:0.863143:0.781606:0.863143:0.781606:0.849427:0.766273:0.849427:0.000000
x:@0.795025:0.863697:0.802480:0.863697:0.802480:0.848262:0.795025:0.848262:0.000000
x:@0.834785:0.863697:0.842240:0.863697:0.842240:0.848262:0.834785:0.848262:0.000000
[:@0.846087:0.863559:0.861420:0.863559:0.861420:0.849510:0.846087:0.849510:0.000000
R:@0.865249:0.862837:0.878539:0.862837:0.878539:0.849940:0.865249:0.849940:0.000000
vertical dada como     {( 1,  ) |      }.:@0.293667:0.880339:0.593687:0.880339:0.593687:0.864626:0.293667:0.864626:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Av:@0.436875:0.880339:0.454104:0.880339:0.454104:0.864904:0.436875:0.864904:0.000000:0.000000
5 2:@0.458007:0.879784:0.502129:0.879784:0.502129:0.866069:0.458007:0.866069:0.000000:0.000000:0.000000
y y:@0.518014:0.880339:0.549399:0.880339:0.549399:0.864904:0.518014:0.864904:0.000000:0.000000:0.000000
[:@0.553283:0.880200:0.568616:0.880200:0.568616:0.866152:0.553283:0.866152:0.000000
R:@0.572481:0.879479:0.585772:0.879479:0.585772:0.866582:0.572481:0.866582:0.000000
Es preciso recalcar que en el cálculo de (     )( ) hemos utilizado las propiedades :@0.293685:0.909130:0.930946:0.909130:0.930946:0.893417:0.293685:0.893417:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.608836:0.909130:0.613530:0.909130:0.613530:0.893694:0.608836:0.893694:0.000000
1:@0.619494:0.908575:0.634827:0.908575:0.634827:0.894859:0.619494:0.894859:0.000000
g x:@0.640864:0.909130:0.667960:0.909130:0.667960:0.893694:0.640864:0.893694:0.000000:0.000000:0.000000
algebraicas de los números reales,  , muy particularmente, las enunciadas en el teorema :@0.293704:0.925771:0.931232:0.925771:0.931232:0.910059:0.293704:0.910059:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.542717:0.925771:0.550190:0.925771:0.550190:0.910336:0.542717:0.910336:0.000000
precedente.:@0.293704:0.942413:0.380729:0.942413:0.380729:0.926701:0.293704:0.926701:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Tema 2. Operaciones con funciones racionales:@0.073089:0.098522:0.753080:0.098522:0.753080:0.067281:0.073089:0.067281:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Es posible realizar una representación gráfica de la función real?:@0.310262:0.178719:0.776795:0.178719:0.776795:0.163007:0.310262:0.163007:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Reto matemático:@0.302768:0.139600:0.437491:0.139600:0.437491:0.122653:0.302768:0.122653:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Aprende las siguientes :@0.082576:0.293928:0.235359:0.293928:0.235359:0.279643:0.082576:0.279643:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
definiciones::@0.082576:0.309057:0.165442:0.309057:0.165442:0.294772:0.082576:0.294772:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sean  ,   dos funciones :@0.082576:0.331334:0.241330:0.331334:0.241330:0.317050:0.082576:0.317050:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p q:@0.118403:0.331334:0.141596:0.331334:0.141596:0.317302:0.118403:0.317302:0.000000:0.000000:0.000000
polinomiales.:@0.082559:0.346463:0.170238:0.346463:0.170238:0.332179:0.082559:0.332179:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La función real  , definida :@0.082559:0.368740:0.250667:0.368740:0.250667:0.354456:0.082559:0.354456:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.182560:0.368740:0.186828:0.368740:0.186828:0.354708:0.182560:0.354708:0.000000
como:@0.082559:0.383869:0.121331:0.383869:0.121331:0.369585:0.082559:0.369585:0.000000:0.000000:0.000000:0.000000
f:@0.082559:0.411391:0.086826:0.411391:0.086826:0.397359:0.082559:0.397359:0.000000
    ,       0,:@0.086759:0.411391:0.176623:0.411390:0.176623:0.397106:0.086759:0.397107:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.090357:0.410887:0.104296:0.410887:0.104296:0.398418:0.090357:0.398418:0.000000
p:@0.111915:0.402706:0.121174:0.402706:0.121174:0.387271:0.111915:0.387271:0.000000
q:@0.111252:0.416935:0.120511:0.416935:0.120511:0.401499:0.111252:0.401499:0.000000
q:@0.136211:0.411390:0.144628:0.411390:0.144628:0.397358:0.136211:0.397358:0.000000
?:@0.148159:0.411882:0.162098:0.411882:0.162098:0.398089:0.148159:0.398089:0.000000
se llama función racional.:@0.082579:0.433667:0.248547:0.433667:0.248547:0.419383:0.082579:0.419383:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Nota que la función :@0.082579:0.455945:0.216668:0.455945:0.216668:0.441660:0.082579:0.441660:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
polinomial   no es nula.:@0.082579:0.471074:0.239593:0.471074:0.239593:0.456789:0.082579:0.456789:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
q:@0.156844:0.471074:0.165261:0.471074:0.165261:0.457042:0.156844:0.457042:0.000000
La función real  , definida:@0.082579:0.493351:0.247023:0.493351:0.247023:0.479067:0.082579:0.479067:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.182581:0.493351:0.186848:0.493351:0.186848:0.479319:0.182581:0.479319:0.000000
como         0, se llama :@0.082579:0.522386:0.257669:0.522382:0.257669:0.508098:0.082579:0.508102:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.124849:0.522386:0.129116:0.522386:0.129116:0.508354:0.124849:0.508354:0.000000
5:@0.132647:0.521882:0.146586:0.521882:0.146586:0.509413:0.132647:0.509413:0.000000
p:@0.154187:0.512188:0.163446:0.512188:0.163446:0.496752:0.154187:0.496752:0.000000
q:@0.153524:0.526417:0.162783:0.526417:0.162783:0.510981:0.153524:0.510981:0.000000
5:@0.168461:0.521878:0.182400:0.521878:0.182400:0.509409:0.168461:0.509409:0.000000
función racional nula y se :@0.082582:0.537511:0.253536:0.537511:0.253536:0.523227:0.082582:0.523227:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
representa simplemente :@0.082582:0.552640:0.247878:0.552640:0.247878:0.538356:0.082582:0.538356:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
con 0, siempre que :@0.082582:0.567769:0.212247:0.567769:0.212247:0.553485:0.082582:0.553485:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
no haya peligro de :@0.082582:0.582898:0.209624:0.582898:0.209624:0.568614:0.082582:0.568614:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
confusión.:@0.082582:0.598027:0.151108:0.598027:0.151108:0.583743:0.082582:0.583743:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Recordemos que si  :@0.082582:0.620304:0.215567:0.620304:0.215567:0.606020:0.082582:0.606020:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a b:@0.082582:0.638673:0.105274:0.638673:0.105274:0.624641:0.082582:0.624641:0.000000:0.000000:0.000000
,      ,       :@0.090765:0.638673:0.194161:0.638669:0.194161:0.624385:0.090765:0.624389:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
[:@0.108470:0.638547:0.122409:0.638547:0.122409:0.625776:0.108470:0.625776:0.000000
R:@0.125589:0.637892:0.137670:0.637892:0.137670:0.626167:0.125589:0.626167:0.000000
a:@0.146814:0.630652:0.156073:0.630652:0.156073:0.615217:0.146814:0.615217:0.000000
b:@0.145857:0.645353:0.155115:0.645353:0.155115:0.629917:0.145857:0.629917:0.000000
[:@0.161546:0.638543:0.175486:0.638543:0.175486:0.625772:0.161546:0.625772:0.000000
R:@0.178665:0.637888:0.190747:0.637888:0.190747:0.626163:0.178665:0.626163:0.000000
⇔:@0.193926:0.638291:0.211363:0.638291:0.211363:0.622847:0.193926:0.622847:0.000000
     0. :@0.211112:0.638669:0.257781:0.638669:0.257781:0.624385:0.211112:0.624385:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b:@0.214542:0.638669:0.222960:0.638669:0.222960:0.624637:0.214542:0.624637:0.000000
?:@0.226156:0.639161:0.240095:0.639161:0.240095:0.625369:0.226156:0.625369:0.000000
Esto es,   :@0.082596:0.661186:0.152858:0.661191:0.152858:0.646907:0.082596:0.646902:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.137644:0.656166:0.146902:0.656166:0.146902:0.640731:0.137644:0.640731:0.000000
b:@0.136686:0.670866:0.145945:0.670866:0.145945:0.655431:0.136686:0.655431:0.000000
está bien definido si y :@0.082576:0.683469:0.229047:0.683469:0.229047:0.669185:0.082576:0.669185:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
solo si el denominador  :@0.082576:0.698598:0.240008:0.698598:0.240008:0.684313:0.082576:0.684313:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b:@0.082576:0.713727:0.090993:0.713727:0.090993:0.699695:0.082576:0.699695:0.000000
   0.:@0.090926:0.713727:0.122988:0.713727:0.122988:0.699442:0.090926:0.699442:0.000000:0.000000:0.000000:0.000000:0.000000
?:@0.094524:0.714218:0.108463:0.714218:0.108463:0.700426:0.094524:0.700426:0.000000
Competencia :@0.078581:0.245849:0.187141:0.245849:0.187141:0.228902:0.078581:0.228902:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática :@0.078581:0.262491:0.176057:0.262491:0.176057:0.245544:0.078581:0.245544:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
DBA 3 (Ev. 1) Reconoce la relación funcional entre variables asociadas a problemas.:@0.485209:0.971366:0.919206:0.971366:0.919206:0.959939:0.485209:0.959939:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
MUESTRA EDITORIAL:@0.248902:0.947499:0.888171:0.113285:0.743922:0.050540:0.104653:0.884754:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 Muestra editorial solo para fines didácticos – Prohibida su venta:@0.095585:0.659700:0.095585:0.341447:0.077558:0.341447:0.077558:0.659700:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000