Решебник по алгебре 8 класс Мерзляк Задание 188

\[\boxed{\text{188\ (188).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

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

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

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

\[:\left( \ \frac{a + b^{\backslash b + a}}{b - a} - \frac{b - a^{\backslash b - a}}{a + b} - \frac{6a^{2}}{b^{2} - a^{2}} \right) =\]

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

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

\[= \frac{3ab - 2b^{2}}{b^{2}(b - a)}\ :\frac{6a^{2} - 4ab}{(a - b)(a + b)} =\]

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

\[= \frac{- a - b}{2ab}\ \]

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

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

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

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

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

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

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

\[= \frac{10a}{a(2a - 1)^{2}(2a + 1)} =\]

\[= \frac{10}{(2a - 1)^{2}(2a + 1)}\]

\[3)\ \frac{10}{(2a - 1)^{2}(2a + 1)}\ :\]

\[:\frac{1}{(1 - 2a)^{2}} = \frac{10(1 - 2a)^{2}}{(2a - 1)^{2}(2a + 1)} =\]

\[= \frac{10}{2a + 1}\]

\[4)\ \frac{10^{\backslash a}}{2a + 1} - \frac{8a - 1}{a(2a + 1)} =\]

\[= \frac{10a - 8a + 1}{a(2a + 1)} =\]

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