Answer
$\frac{1}{4(x-2)}$
Work Step by Step
We simplify:
$\displaystyle \frac{4x}{x^{2}-4}*\frac{x+2}{16x}=\frac{4x}{(x-2)(x+2)}*\frac{x+2}{16x}=\frac{1}{4(x-2)}$
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