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