Решебник по алгебре 9 класс Макарычев Задание 924

\[\boxed{\text{924\ (924).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[\textbf{а)}\ \frac{x - y}{x\sqrt{y} - y\sqrt{x}} = \frac{\sqrt{y}}{y} + \frac{\sqrt{x}}{x}\]

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

\[\frac{\left( \sqrt{x} - \sqrt{y} \right)\left( \sqrt{x} + \sqrt{y} \right)}{\sqrt{\text{xy}} \cdot \left( \sqrt{x} - \sqrt{y} \right)} = \frac{\sqrt{y}}{y} + \frac{\sqrt{x}}{x}\]

\[\frac{\sqrt{x} + \sqrt{y}}{\sqrt{\text{xy}}} = \frac{1}{\sqrt{y}} + \frac{1}{\sqrt{x}}\]

\[\frac{\sqrt{y}}{y} + \frac{\sqrt{x}}{x} = \frac{\sqrt{y}}{y} + \frac{\sqrt{x}}{x} \Longrightarrow ч.т.д.\]

\[\textbf{б)}\ \frac{a - b}{a\sqrt{b} + b\sqrt{a}} = \frac{\sqrt{b}}{b} - \frac{\sqrt{a}}{a}\]

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

\[\frac{\left( \sqrt{a} - \sqrt{b} \right)\left( \sqrt{a} + \sqrt{b} \right)}{\sqrt{\text{ab}} \cdot \left( \sqrt{a} + \sqrt{b} \right)} = \frac{\sqrt{b}}{b} - \frac{\sqrt{a}}{a}\]

\[\frac{\sqrt{a} - \sqrt{b}}{\sqrt{\text{ab}}} = \frac{1}{\sqrt{b}} - \frac{1}{\sqrt{a}}\]

\[\frac{\sqrt{b}}{b} - \frac{\sqrt{a}}{a} = \frac{\sqrt{b}}{b} - \frac{\sqrt{a}}{a} \Longrightarrow ч.т.д.\]