Answer
$-\dfrac{32}{x(x+2)(x-2)}$
Work Step by Step
The given expression, $
\dfrac{4}{x}\cdot\left( \dfrac{2}{x+2}-\dfrac{2}{x-2} \right)
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{4}{x}\cdot\dfrac{(x-2)(2)-(x+2)(2)}{(x+2)(x-2)}
\\\\=
\dfrac{4}{x}\cdot\dfrac{2x-4-(2x+4)}{(x+2)(x-2)}
\\\\=
\dfrac{4}{x}\cdot\dfrac{2x-4-2x-4}{(x+2)(x-2)}
\\\\=
\dfrac{4}{x}\cdot\dfrac{-8}{(x+2)(x-2)}
\\\\=
\dfrac{-32}{x(x+2)(x-2)}
\\\\=
-\dfrac{32}{x(x+2)(x-2)}
.\end{array}
