ГДЗ по алгебре 8 класс Макарычев Задание 164

\[\boxed{\text{164\ (164).\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[\textbf{а)}\ \frac{1^{\backslash x} - \frac{1}{x}}{1^{\backslash x} + \frac{1}{x}} = \frac{\frac{x - 1}{x}}{\frac{x + 1}{x}} =\]

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

\[\textbf{б)}\ \frac{\frac{2a - b}{b} + 1^{\backslash b}}{\frac{2a + b}{b} - 1^{\backslash b}} = \frac{\frac{2a - b + b}{b}}{\frac{2a + b - b}{b}} =\]

\[= \frac{2a}{b} \cdot \frac{b}{2a} = 1\]

\[\textbf{в)}\ \frac{\frac{x^{\backslash x^{2}}}{y^{2}} + \frac{y^{\backslash y^{2}}}{x^{2}}}{\frac{x^{\backslash x^{2}}}{y^{2}} - \frac{y^{\backslash y^{2}}}{x^{2}}} = \frac{\frac{x^{3} + y^{3}}{x^{2}y^{2}}}{\frac{x^{3} - y^{3}}{x^{2}y^{2}}} =\]

\[= \frac{x^{3} + y^{3}}{x^{2}y^{2}} \cdot \frac{x^{2}y^{2}}{x^{3} - y^{3}} = \frac{x^{3} + y^{3}}{x^{3} - y^{3}}\ \]

\[\textbf{г)}\ \frac{\frac{1^{\backslash bc}}{a} + \frac{1^{\backslash ac}}{b} + \frac{1^{\backslash ab}}{c}}{\frac{1^{\backslash c}}{\text{ab}} + \frac{1^{\backslash a}}{\text{bc}} + \frac{1^{\backslash b}}{\text{ac}}} =\]

\[= \frac{bc + ac + ab}{\text{abc}}\ :\frac{c + a + b}{\text{abc}} =\]

\[= \frac{bc + ac + ab}{\text{abc}} \cdot \frac{\text{abc}}{c + a + b} =\]

\[= \frac{bc + ac + ab}{c + a + b} = \frac{ab + bc + ac}{a + b + c}\]