ГДЗ по математике 6 класс Мерзляк Задание 489

\[\boxed{\mathbf{489\ (489).}\mathbf{\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

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

\[= 2 + \frac{1}{1 + \frac{2}{1\frac{1}{3}}} = 2 + \frac{1}{1 + \frac{2}{\frac{4}{3}}} =\]

\[= 2 + \frac{1}{1 + \frac{6}{4}} = 2 + \frac{1}{1\frac{6}{4}} =\]

\[= 2 + \frac{1}{\frac{10}{4}} = 2 + \frac{4}{10} = 2\frac{4}{10} =\]

\[= 2\frac{2}{5}\]

\[2)\ \frac{2 - \frac{\frac{1^{\backslash 2}}{2} - \frac{1}{4}}{2}}{2 + \frac{\frac{1^{\backslash 2}}{2} - \frac{1}{4}}{2}} = \frac{2 - \frac{\frac{2 - 1}{4}}{2}}{2 + \frac{\frac{2 - 1}{4}}{2}} =\]

\[= \frac{2 - \frac{\frac{1}{4}}{2}}{2 + \frac{\frac{1}{4}}{2}} = \frac{2 - \frac{1}{8}}{2 + \frac{1}{8}} = \frac{1\frac{7}{8}}{2\frac{1}{8}} = \frac{\frac{15}{8}}{\frac{17}{8}} =\]

\[= \frac{15}{8} \cdot \frac{8}{17} = \frac{15}{17}\]

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

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

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

\[= \frac{1}{2 - \frac{1}{\frac{7}{5}}} = \frac{1}{2 - \frac{5}{7}} = \frac{1}{1\frac{2}{7}} = \frac{1}{\frac{9}{7}} =\]

\[= 1 \cdot \frac{7}{9} = \frac{7}{9}\]