Answer
$\dfrac{(x+2)^{2}}{x-2}\div\dfrac{x^{2}-4}{2x-4}=\dfrac{2(x+2)}{x-2}$
Work Step by Step
$\dfrac{(x+2)^{2}}{x-2}\div\dfrac{x^{2}-4}{2x-4}$
Factor the second fraction completely:
$\dfrac{(x+2)^{2}}{x-2}\div\dfrac{x^{2}-4}{2x-4}=\dfrac{(x+2)^{2}}{x-2}\div\dfrac{(x-2)(x+2)}{2(x-2)}=...$
Evaluate the division of the two rational expressions and simplify by removing the factors that appear both in the numerator and the denominator of the resulting expression:
$...=\dfrac{2(x-2)(x+2)^{2}}{(x-2)^{2}(x+2)}=\dfrac{2(x+2)}{x-2}$
