Решебник по алгебре 9 класс Мерзляк Задание 866

\[\boxed{\mathbf{866\ (866).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ \frac{2}{x + y} + \frac{3}{x - y} =\]

\[= \frac{2 \cdot (x - y) + 3 \cdot (x + y)}{(x + y)(x - y)} =\]

\[= \frac{2x - 2y + 3x + 3y}{(x + y)(x - y)} = \frac{5x + y}{x^{2} - y^{2}}\]

\[2)\ \frac{a + 1}{a - 4} + \frac{a - 1}{a - 6} =\]

\[= \frac{(a + 1)(a - 6) + (a - 1)(a - 4)}{(a - 4)(a - 6)} =\]

\[= \frac{a^{2} - 6a + a - 6 + a^{2} - 4a - a + 4}{(a - 4)(a - 6)} =\]

\[= \frac{2a² - 10a - 2}{a^{2} - 10a + 24}\]

\[3)\ \frac{c - 7}{c + 1} - \frac{c - 3}{c - 5} =\]

\[= \frac{(c - 7)(c - 5) - (c - 3)(c + 1)}{(c + 1)(c - 5)} =\]

\[= \frac{c^{2} - 5c - 7c + 35 - c^{2} - c + 3c + 3}{(c + 1)(c - 5)} =\]

\[= \frac{- 10c + 38}{(c + 1)(c - 5)} = \frac{38 - 10c}{c^{2} - 4c - 5}\]