Answer
$\dfrac{-x+10}{3(x-5)(5+x)}$
Work Step by Step
Factoring the given expression, $
\dfrac{x}{25-x^2}+\dfrac{2}{3x-15}
,$ results to
\begin{array}{l}
\dfrac{x}{(5-x)(5+x)}+\dfrac{2}{3(x-5)}
\\\\=
\dfrac{x}{-(x-5)(5+x)}+\dfrac{2}{3(x-5)}
\\\\=
-\dfrac{x}{(x-5)(5+x)}+\dfrac{2}{3(x-5)}
.\end{array}
Using the $LCD=
3(x-5)(5+x)$, the expression above simplifies to
\begin{array}{l}
\dfrac{3(-x)+(5+x)(2)}{3(x-5)(5+x)}
\\\\=
\dfrac{-3x+10+2x}{3(x-5)(5+x)}
\\\\=
\dfrac{-x+10}{3(x-5)(5+x)}
.\end{array}
