ГДЗ по алгебре 8 класс Макарычев Задание 67

\[\boxed{\text{67\ (67).\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[Тождество:\]

\[\frac{a + b}{c} = \frac{a}{c} + \frac{b}{c};\]

\[\frac{a - b}{c} = \frac{a}{c} - \frac{b}{c}.\]

Решение.

\[\textbf{а)}\ \frac{x^{2} + y^{2}}{x^{4}} = \frac{x^{2}}{x^{4}} + \frac{y^{2}}{x^{4}} = \frac{1}{x^{2}} + \frac{y^{2}}{x^{4}}\]

\[\textbf{б)}\ \frac{2x - y}{b} = \frac{2x}{b} - \frac{y}{b}\]

\[\textbf{в)}\ \frac{a^{2} + 1}{2a} = \frac{a^{2}}{2a} + \frac{1}{2a} = \frac{a}{2} + \frac{1}{2a}\]

\[\textbf{г)}\ \frac{a^{2} - 3ab}{a^{3}} = \frac{a(a - 3b)}{a^{3}} =\]

\[= \frac{a - 3b}{a^{2}} = \frac{a}{a^{2}} - \frac{3b}{a^{2}} = \frac{1}{a} - \frac{3b}{a^{2}}\]