Упростите упражнение: ((a+4)/(a-4)-(a-4)/(a+4)):48a/(16-a^2).

\[\left( \frac{a + 4^{\backslash a + 4}}{a - 4} - \frac{a - 4^{\backslash a - 4}}{a + 4} \right)\ :\frac{48a}{16 - a^{2}} =\]

\[= \frac{a^{2} + 8a + 16 - a^{2} + 8a - 16}{(a - 4)(a + 4)} \cdot \frac{16 - a^{2}}{48a} =\]

\[= \frac{16a \cdot \left( 16 - a^{2} \right)}{\left( a^{2} - 16 \right) \cdot 48a} = - \frac{1}{3}\text{.\ }\]