Answer
$\dfrac{-7x-6}{5(x-3)(x+3)}$
Work Step by Step
Factoring the given expression, $
\dfrac{x}{9-x^2}-\dfrac{2}{5x-15}
,$ results to
\begin{array}{l}\require{cancel}
\dfrac{x}{-(x^2-9)}-\dfrac{2}{5x-15}
\\\\=
\dfrac{x}{-(x-3)(x+3)}-\dfrac{2}{5(x-3)}
\\\\=
\dfrac{-x}{(x-3)(x+3)}-\dfrac{2}{5(x-3)}
.\end{array}
Using the $LCD=
5(x-3)(x+3)
$, the expression above simplifies to
\begin{array}{l}\require{cancel}
\dfrac{5(-x)-(x+3)(2)}{5(x-3)(x+3)}
\\\\=
\dfrac{-5x-2x-6}{5(x-3)(x+3)}
\\\\=
\dfrac{-7x-6}{5(x-3)(x+3)}
.\end{array}
