Упростите упражнение: ((a-1)/(a+1)-(a+1)/(a-1)):2a/(1-a^2).

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

\[= \frac{a^{2} - 2a + 1 - a^{2} - 2a - 1}{(a + 1)(a - 1)} \cdot \frac{1 - a^{2}}{2a} =\]

\[= - \frac{4a}{a^{2} - 1} \cdot \frac{1 - a^{2}}{2a} = 2.\]