Question

resuelva la suma de fracciones algebraicas x+5/x^2-3x-4 + x-4/x^2-4x-5

Answer 1

$\frac{\left(x+5\right)}{x^2-3x-4}+\frac{x-4}{x^2-4x-5}$
factorizamos  aparte
$x^2-3x-4=\left(x+1\right)\left(x-4\right)$
$x^2-4x-5=\left(x+1\right)\left(x-5\right)$
queda
$\frac{\left(x+5\right)}{x^2-3x-4}+\frac{x-4}{x^2-4x-5}=\frac{x+5}{\left(x+1\right)\left(x-4\right)}+\frac{x-4}{\left(x+1\right)\left(x-5\right)}$
$=\frac{\left(x+5\right)\left(x-5\right)+\left(x-4\right)\left(x-4\right)}{\left(x+1\right)\left(x-5\right)\left(x-4\right)}$

desarrollando el numerador
$x^2-25+x^2-8x+16=2x^2-8x-9$

$=\frac{2x^2-8x-9}{\left(x+1\right)\left(x-5\right)\left(x-4\right)}$