Решебник по математике 6 класс Мерзляк ФГОС Задание 316

\[\boxed{\mathbf{316\ (317).}\mathbf{\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

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

\[\frac{1}{6} = \frac{3a - 2b}{6}\]

\[3a - 2b = 1\]

\[a = b = 1.\]

\[2)\ \frac{4}{3 \cdot 5} = \frac{a}{3} - \frac{b}{5}\]

\[\frac{4}{15} = \frac{5a - 3b}{15}\]

\[5a - 3b = 4\]

\[a = b = 2.\]

\[\boxed{\mathbf{316\ (}\mathbf{с}\mathbf{).}\mathbf{\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ a + \frac{1}{a} = 7\frac{1}{7}\]

\[7 + \frac{1}{7} = 7\frac{1}{7}\]

\[\Longrightarrow a = 7.\]

\[2)\ b - \frac{1}{b} = 14\frac{14}{15}\]

\[15 - \frac{1}{15} = 14\frac{14}{15}\]

\[\Longrightarrow b = 15.\]

\[\boxed{\mathbf{316}\mathbf{.}}\]

\[\frac{1}{7};\ \frac{2}{7};\ \frac{3}{7};\ \frac{4}{7};\ \frac{5}{7};\ \frac{6}{7}.\]