Answer
$\dfrac{x+8}{x^{2}-5x-6}+\dfrac{x+1}{x^{2}-4x-5}=\dfrac{2(x^{2}-x-23)}{(x+1)(x-6)(x-5)}$
Work Step by Step
$\dfrac{x+8}{x^{2}-5x-6}+\dfrac{x+1}{x^{2}-4x-5}$
Factor the denominator of both rational expressions:
$\dfrac{x+8}{x^{2}-5x-6}+\dfrac{x+1}{x^{2}-4x-5}=\dfrac{x+8}{(x-6)(x+1)}+\dfrac{x+1}{(x-5)(x+1)}$
Evaluate the sum of the two rational expressions and simplify:
$...=\dfrac{(x+8)(x-5)+(x+1)(x-6)}{(x+1)(x-6)(x-5)}=...$
$...=\dfrac{x^{2}+3x-40+x^{2}-5x-6}{(x+1)(x-6)(x-5)}=\dfrac{2x^{2}-2x-46}{(x+1)(x-6)(x-5)}=...$
Take out common factor $2$ from the numerator to provide a more simplified answer:
$...=\dfrac{2(x^{2}-x-23)}{(x+1)(x-6)(x-5)}$
