Решебник по алгебре 8 класс Мерзляк Задание 867

\[\boxed{\mathbf{867\ (867).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\left( \frac{a + 4}{a - 4} - \frac{a - 4}{a + 4} \right) \cdot \frac{16 - a^{2}}{32a^{3}} =\]

\[= \frac{- 16a(a - 4)(a + 4)}{32a^{3}(a - 4)(a + 4)} = - \frac{1}{2a^{2}}\]

\[2)\ \left( 7x - \frac{4x}{x - 3} \right)\ :\frac{14x - 50}{3x - 9} =\]

\[= \frac{7x^{2} - 25x}{x - 3}\ :\frac{14x - 50}{3x - 9} =\]

\[= \frac{x(7x - 25) \cdot 3 \cdot (x - 3)}{(x - 3) \cdot 2 \cdot (7x - 25)} = \frac{3x}{2}\ \]

\[3)\ \frac{2a}{a - 2} + \frac{a + 7}{8 - 4a} \cdot \frac{32}{7a + a^{2}} =\]

\[= \frac{2a}{a - 2} - \frac{32}{4a(a - 2)} =\]

\[= \frac{8a^{2} - 32}{4a(a - 2)} =\]

\[= \frac{8 \cdot (a - 2)(a + 2)}{4a(a - 2)} = \frac{2a + 4}{a}\]

\[1)\frac{9c}{c - 8} + \frac{7c}{(c - 8)^{2}} =\]

\[= \frac{9c^{2} - 72c + 7c}{(c - 8)^{2}} = \frac{9c^{2} - 65c}{(c - 8)^{2}}\]

\[2)\ \frac{c(9c - 65)(c - 8)(c + 8)}{(c - 8)^{2}(9c - 65)} =\]

\[= \frac{c(c + 8)}{c - 8}\]

\[3)\ \frac{c^{2} + 8c - 8c - 64}{c - 8} =\]

\[= \frac{(c - 8)(c + 8)}{(c - 8)} = c + 8\]

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

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

\[= \frac{a^{2} + ab - a^{2}}{(a - b)(a + b)} =\]

\[= \frac{\text{ab}}{(a - b)(a + b)}\ \]

\[3)\ \frac{a²b(a - b)(a + b)}{\text{ab}(a + b)²} = \frac{a(a - b)}{a + b}\]

\[= \frac{- \left( b^{2} + 12b + 36 \right)}{(b + 6)(b - 6)} =\]

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

\[= \frac{- b - 6}{b - 6}\]

\[2)\ \frac{- (b + 6)(6 - b)²}{(b - 6) \cdot b(6 + b)} = \frac{6 - b}{b}\]

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

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

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

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

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

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

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

\[4)\frac{(x - 1)(x + 1)}{2 \cdot (x + 1)(x - 1)} = \frac{1}{2}\ \]