Упростите выражение: (a/(a-4)-a/(a+4)-(a^2+16)/(16-a^2)):(4a+a^2)/(4-a)^2.

\[\left( \frac{a^{\backslash a + 4}}{a - 4} - \frac{a^{\backslash a - 4}}{a + 4} - \frac{a^{2} + 16^{\backslash\text{-}1}}{16 - a^{2}} \right)\ :\frac{4a + a^{2}}{(4 - a)^{2}} =\]

\[= \frac{a^{2} + 4a - a^{2} + 4a + a^{2} + 16}{(a - 4)(a + 4)} \cdot \frac{(4 - a)^{2}}{4a + a^{2}} =\]

\[= \frac{a^{2} + 8a + 16}{a^{2} - 16} \cdot \frac{(a - 4)^{2}}{a(4 + a)} =\]

\[= \frac{(a + 4)^{2}(a - 4)^{2}}{(a - 4)(a + 4)a(a + 4)} =\]

\[= \frac{a - 4}{a}.\]