Решебник по алгебре 8 класс Мерзляк Задание 176

\[\boxed{\text{176\ (176).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[1)\left( \frac{a^{\backslash 4}}{3} + \frac{a^{\backslash 3}}{4} \right) \cdot \frac{6}{a^{2}} = \frac{4a + 3a}{12} \cdot\]

\[\cdot \frac{6}{a^{2}} = \frac{7a \cdot 6}{12a^{2}} = \frac{7}{2a}\]

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

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

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

\[= \frac{b + a}{b}\ :\frac{b - a}{b} = \frac{(b + a) \cdot b}{(b - a) \cdot b} =\]

\[= \frac{b + a}{b - a}\]

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

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

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

\[5)\ \frac{a^{2} - ab}{b^{2} - 1} \cdot \frac{b + 1}{a} - \frac{a}{b - 1} =\]

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

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

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

\[6)\ \left( \frac{5^{\backslash m + n}}{m - n} - \frac{4^{\backslash m - n}}{m + n} \right)\ :\frac{m + 9n}{m + n} =\]

\[= \frac{5(m + n) - 4(m - n)}{(m - n)(m + n)}\ :\]

\[:\frac{m + 9n}{m + n} =\]

\[= \frac{(m + 9n)(m + n)}{(m - n)(m + n)(m + 9n)} =\]

\[= \frac{1}{m - n}\]

\[7)\ \frac{x - 2}{x + 2} \cdot \left( x^{\backslash x - 2} - \frac{x^{2}}{x - 2} \right) =\]

\[= \frac{x - 2}{x + 2} \cdot \frac{x^{2} - 2x - x^{2}}{x - 2} =\]

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

\[8)\ \frac{x^{2} + x}{4}\ :\frac{x^{2}}{4} + \frac{x - 1}{x} =\]

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

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

\[9)\ \frac{6c^{2}}{c^{2} - 1}\ :\left( \frac{1}{c - 1} + 1^{\backslash c - 1} \right) =\]

\[= \frac{6c^{2}}{c^{2} - 1}\ :\frac{1 + c - 1}{c - 1} =\]

\[= \frac{6c^{2}(c - 1)}{c(c - 1)(c + 1)} = \frac{6c}{c + 1}\]

\[10)\ \left( \frac{x^{\backslash x - y}}{x + y} + \frac{y^{\backslash x + y}}{x - y} \right) \cdot\]

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

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

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

\[= \frac{x}{x - y}\]