ГДЗ по математике 6 класс Мерзляк Задание 488

\[\boxed{\mathbf{488\ (488).}\mathbf{\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ 1 - \frac{2}{3 + \frac{1}{2}} = 1 - \frac{2}{3\frac{1}{2}} =\]

\[= 1 - \frac{2}{\frac{7}{2}} = 1 - \frac{2 \cdot 2}{7} = 1 - \frac{4}{7} =\]

\[= \frac{7}{7} - \frac{3}{7} = \frac{3}{7}\]

\[2)\ \frac{8 - \frac{1}{\frac{1^{\backslash 3}}{2} - \frac{1^{\backslash 2}}{3}}}{8 + \frac{1}{\frac{1^{\backslash 3}}{2} - \frac{1^{\backslash 2}}{3}}} = \frac{8 - \frac{1}{\frac{3 - 2}{6}}}{8 + \frac{1}{\frac{3 - 2}{6}}} =\]

\[= \frac{8 - \frac{1}{\frac{1}{6}}}{8 + \frac{1}{\frac{1}{6}}} = \frac{8 - 6}{8 + 6} = \frac{2}{14} = \frac{1}{7}\]

\[3)\ \frac{1}{1 + \frac{1}{1 + \frac{1}{1 + \frac{1}{2}}}} = \frac{1}{1 + \frac{1}{1 + \frac{1}{1\frac{1}{2}}}} =\]

\[= \frac{1}{1 + \frac{1}{1 + \frac{1}{\frac{3}{2}}}} = \frac{1}{1 + \frac{1}{1 + \frac{2}{3}}} =\]

\[= \frac{1}{1 + \frac{1}{1\frac{2}{3}}} = \frac{1}{1 + \frac{1}{\frac{5}{3}}} = \frac{1}{1 + \frac{5}{3}} =\]

\[= \frac{1}{1\frac{3}{5}} = \frac{1}{\frac{8}{5}} = \frac{5}{8}\]