Упростите выражение: (a+3)/(4a+4)-(a+1)/(4a-4)-a/(1-a^2).

Ответ:

\[\frac{a + 3}{4a + 4} - \frac{a + 1}{4a - 4} - \frac{a}{1 - a^{2}} =\]

\[= \frac{a + 3^{\backslash a - 1}}{4(a + 1)} - \frac{a + 1^{\backslash a + 1}}{4(a - 1)} + \frac{a^{\backslash 4}}{a^{2} - 1} =\]

\[= \frac{a^{2} + 3a - a - 3 - a^{2} - 2a - 1 + 4a}{4\left( a^{2} - 1 \right)} =\]

\[= \frac{4a - 4}{4\left( a^{2} - 1 \right)} =\]

\[= \frac{4(a - 1)}{4(a - 1)(a + 1)} = \frac{1}{a + 1}.\]