Answer
$x=7$
Work Step by Step
$\dfrac{4}{x+5}+\dfrac{2}{x-5}=\dfrac{32}{x^{2}-25}$
Factor the denominator of the fraction on the right side:
$\dfrac{4}{x+5}+\dfrac{2}{x-5}=\dfrac{32}{(x-5)(x+5)}$
Multiply the whole equation by $(x-5)(x+5)$:
$(x+5)(x-5)\Big[\dfrac{4}{x+5}+\dfrac{2}{x-5}=\dfrac{32}{(x-5)(x+5)}\Big]$
$4(x-5)+2(x+5)=32$
$4x-20+2x+10=32$
Take all terms without $x$ to the right side, simplify, and solve for $x$:
$4x+2x=32-10+20$
$6x=42$
$x=\dfrac{42}{6}$
$x=7$
