Решебник по алгебре 8 класс Макарычев ФГОС Задание 1254

\[\boxed{\text{1254.\ }\text{еуроки}\text{-}\text{ответы}\text{\ }\text{на}\text{\ }\text{пятёрку}}\]

\[\textbf{а)}\ \frac{x^{- 1} + y^{- 1}}{(x + y)^{2}} = \frac{\frac{1}{x} + \frac{1}{y}}{(x + y)^{2}} =\]

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

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

\[\textbf{б)}\ \frac{ab^{- 1} - a^{- 1}b}{a^{- 1} - b^{- 1}} = \frac{\frac{a}{b} - \frac{b}{a}}{\frac{1}{a} - \frac{1}{b}} =\]

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

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

\[= - a - b\]