Найдите значение выражения:
а) $\frac{6 - \frac{1}{\frac{1}{2} - \frac{1}{3}}}{6 + \frac{1}{\frac{1}{2} - \frac{1}{3}}}$;
б) $2 + \frac{1}{1 + \frac{2}{1 + \frac{1}{3}}}$;
в) $\frac{1}{1 + \frac{1}{1 + \frac{1}{1 + \frac{1}{3}}}}$.
$\frac{6 - \frac{1}{\frac{1}{2} - \frac{1}{3}}}{6 + \frac{1}{\frac{1}{2} - \frac{1}{3}}} = \frac{6 - \frac{1}{\frac{3 - 2}{6}}}{6 + \frac{1}{\frac{3 - 2}{6}}} = \frac{6 - 1 : \frac{1}{6}}{6 + 1 : \frac{1}{6}} = \frac{6 - 1 * 6}{6 + 1 * 6} = \frac{6 - 6}{6 + 6} = \frac{0}{12} = 0$
$2 + \frac{1}{1 + \frac{2}{1 + \frac{1}{3}}} = 2 + \frac{1}{1 + 2 : 1\frac{1}{3}} = 2 + \frac{1}{1 + 2 : \frac{4}{3}} = 2 + \frac{1}{1 + 2 * \frac{3}{4}} = 2 + \frac{1}{1 + \frac{3}{2}} = 2 + \frac{1}{1 + 1\frac{1}{2}} = 2 + \frac{1}{2\frac{1}{2}} = 2 + 1 : \frac{5}{2} = 2 + 1 * \frac{2}{5} = 2 + \frac{2}{5} = 2\frac{2}{5}$
$\frac{1}{1 + \frac{1}{1 + \frac{1}{1 + \frac{1}{3}}}} = \frac{1}{1 + \frac{1}{1 + \frac{1}{1\frac{1}{3}}}} = \frac{1}{1 + \frac{1}{1 + 1 : \frac{4}{3}}} = \frac{1}{1 + \frac{1}{1 + 1 * \frac{3}{4}}} = \frac{1}{1 + \frac{1}{1\frac{3}{4}}} = \frac{1}{1 + 1 : 1\frac{3}{4}} = \frac{1}{1 + 1 : \frac{7}{4}} = \frac{1}{1 + 1 * \frac{4}{7}} = \frac{1}{1 + \frac{4}{7}} = \frac{1}{1\frac{4}{7}} = 1 : 1\frac{4}{7} = 1 : \frac{11}{7} = 1 * \frac{7}{11} = \frac{7}{11}$
Пожауйста, оцените решение
