ГДЗ по алгебре 8 класс Макарычев Задание 165

\[\boxed{\text{165\ (165).\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[\textbf{а)}\ \frac{2^{\backslash x} - \frac{a}{x}}{2^{\backslash x} + \frac{a}{x}} = \frac{2x - a}{x}\ :\frac{2x + a}{x} =\]

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

\[\textbf{б)}\ \frac{\frac{a - b}{c} + 3^{\backslash c}}{\frac{a + b}{c} - 1^{\backslash c}} =\]

\[= \frac{a - b + 3c}{c}\ :\frac{a + b - c}{c} =\]

\[= \frac{a - b + 3c}{c} \cdot \frac{c}{a + b - c} =\]

\[= \frac{a - b + 3c}{a + b - c}\]

\[\textbf{в)}\ \frac{\frac{1^{\backslash y}}{x} + \frac{1^{\backslash x}}{y}}{\frac{1^{\backslash y}}{x} - \frac{1^{\backslash x}}{y}} = \frac{y + x}{\text{xy}}\ :\frac{y - x}{\text{xy}} =\]

\[= \frac{y + x}{\text{xy}} \cdot \frac{\text{xy}}{y - x} = \frac{y + x}{y - x}\]

\[\textbf{г)}\ \frac{x - y}{\frac{x^{\backslash x}}{y} - \frac{y^{\backslash y}}{x}} =\]

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

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

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