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}$