Упростите выражение ((a-1)/(a+1)-(a+1)/(a-1))∶2a/(1-a^2).

Ответ:

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

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

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

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