Answer
$\frac{(x+2)^2}{6}$, with $x\ne2$
Work Step by Step
$\frac{x^2-4}{12}\div\frac{2-x}{2x+4}=\frac{x^2-4}{12}\frac{2x+4}{x-2}=\frac{(x+2)(x-2)}{2(6)}\frac{2(x+2)}{x-2}=\frac{(x+2)^2}{6}$
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