Answer
$x=-\dfrac{2}{3}$
Work Step by Step
Expressing the terms of the given equation, $
\dfrac{3}{x^2-25}=\dfrac{1}{x+5}+\dfrac{2}{x-5}
,$ in factored form results to
\begin{array}{l}\require{cancel}
\dfrac{3}{(x+5)(x-5)}=\dfrac{1}{x+5}+\dfrac{2}{x-5}
.\end{array}
Multiplying both sides by the $LCD=
(x+5)(x-5)
$, then the solution to the equation above is
\begin{array}{l}
1(3)=(x-5)(1)+(x+5)(2)
\\\\
3=x-5+2x+10
\\\\
-x-2x=-5+10-3
\\\\
-3x=2
\\\\
x=\dfrac{2}{-3}
\\\\
x=-\dfrac{2}{3}
.\end{array}
