Question

$( \frac{a-2}{a+2} - \frac{a+2}{a-2} ) : \frac{12a}{4-a^{2} }$

Answer 1

$( \frac{a-2}{a+2}- \frac{a+2}{a-2}): \frac{12a}{4-a^2} = \frac{(a-2)^2-(a+2)^2}{(a+2)(a-2)}* \frac{4-a^2}{12a}= \frac{(a-2+a+2)(a-2-a-2)}{a^2-4} * \frac{4-a^2}{12a}$$= \frac{2a*(-4)}{a^2-4} * \frac{4-a^2}{12a} = \frac{-8a}{-(4-a^2)}* \frac{4-a^2}{12a}= \frac{8a*(4-a^2)}{(4-a^2)*12a} = \frac{2}{3}$