Вычислите: ((a-2)/(2+a)+(a+2)/(2-a)):12a^2/(4-a^2).

\[\left( \frac{a - 2^{\backslash 2 - a}}{2 + a} + \frac{a + 2^{\backslash 2 + a}}{2 - a} \right)\ :\frac{12a^{2}}{4 - a^{2}} =\]

\[= \frac{- \left( a^{2} - 4a + 4 \right) + a^{2} + 4a + 4}{(2 + a)(2 - a)} \cdot \frac{4 - a^{2}}{12a^{2}} =\]

\[= \frac{- a^{2} + 4a - 4 + a^{2} + 4a + 4}{4 - a^{2}} \cdot \frac{4 - a^{2}}{12a^{2}} =\]

\[= \frac{8a}{12a^{2}} = \frac{2}{3a}.\]