Answer
$\dfrac{x(x-2)}{2(x+2)}$
Work Step by Step
The expression $
\dfrac{\dfrac{5x}{x+2}}{\dfrac{10}{x-2}}
$ simplifies to
\begin{array}{l}
\dfrac{5x}{x+2}\div\dfrac{10}{x-2}
\\\\=
\dfrac{5x}{x+2}\cdot\dfrac{x-2}{10}
\\\\=
\dfrac{5\cdot x(x-2)}{5\cdot2(x+2)}
\\\\=
\dfrac{x(x-2)}{2(x+2)}
.\end{array}
