Answer
$\dfrac{8}{x^{2}+6x+5}-\dfrac{3x}{x^{2}+4x-5}+\dfrac{2}{x^{2}-1}=-\dfrac{3x^{2}-7x-2}{(x+5)(x+1)(x-1)}$
Work Step by Step
$\dfrac{8}{x^{2}+6x+5}-\dfrac{3x}{x^{2}+4x-5}+\dfrac{2}{x^{2}-1}$
Factor the three rational expressions completely:
$\dfrac{8}{(x+5)(x+1)}-\dfrac{3x}{(x+5)(x-1)}+\dfrac{2}{(x-1)(x+1)}=...$
Evaluate the indicated operations and simplify:
$...=\dfrac{8(x-1)-3x(x+1)+2(x+5)}{(x+5)(x+1)(x-1)}=...$
$...=\dfrac{8x-8-3x^{2}-3x+2x+10}{(x+5)(x+1)(x-1)}=\dfrac{-3x^{2}+7x+2}{(x+5)(x+1)(x-1)}=...$
$...=-\dfrac{3x^{2}-7x-2}{(x+5)(x+1)(x-1)}$
