Решебник по алгебре 8 класс Мерзляк Задание 184

\[\boxed{\text{184\ (184).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

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

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

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

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

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

\[Ответ:не\ зависит.\]

\[2)\ \left( \frac{a}{a^{2} - 49} - \frac{1}{a + 7} \right)\ :\]

\[:\frac{7a}{a^{2} + 14a + 49} - \frac{2}{a - 7} =\]

\[= \left( \frac{a}{(a - 7)(a + 7)} - \frac{1^{\backslash a - 7}}{a + 7} \right)\ :\]

\[:\frac{7a}{(a + 7)^{2}} - \frac{2}{a - 7} =\]

\[= \frac{a - a + 7}{(a - 7)(a + 7)} \cdot \frac{(a + 7)^{2}}{7a} -\]

\[- \frac{2}{a - 7} = \frac{7 \cdot (a + 7)^{2}}{7a(a - 7)(a + 7)} -\]

\[- \frac{2}{a - 7} =\]

\[= \frac{a + 7}{a(a - 7)} - \frac{2^{\backslash a}}{a - 7} =\]

\[= \frac{a + 7 - 2a}{a(a - 7)} = \frac{- a + 7}{a(a - 7)} =\]

\[= - \frac{1}{a}\ \]

\[Ответ:зависит.\]