Найдите значение выражения: a) 1/(1+1/2+1/4) : (2+1/(1/2+1/4)); б) 1-1/(1+1/2); д) 1+1/(1+1/(1+1/2)); г) 2 + 2/(1-2/3); e) 3-3/(3-1/(1-1/3)).

a) $$\frac{1}{1+\frac{1}{2}+\frac{1}{4}} : \left(2+\frac{1}{\frac{1}{2}+\frac{1}{4}}\right) = \frac{1}{\frac{4}{4}+\frac{2}{4}+\frac{1}{4}} : \left(2+\frac{1}{\frac{2}{4}+\frac{1}{4}}\right) = \frac{1}{\frac{7}{4}} : \left(2+\frac{1}{\frac{3}{4}}\right) = \frac{4}{7} : \left(2+\frac{4}{3}\right) = \frac{4}{7} : \left(\frac{6}{3}+\frac{4}{3}\right) = \frac{4}{7} : \frac{10}{3} = \frac{4}{7} \cdot \frac{3}{10} = \frac{12}{70} = \frac{6}{35}$$

б) $$1-\frac{1}{1+\frac{1}{2}} = 1 - \frac{1}{\frac{2}{2}+\frac{1}{2}} = 1 - \frac{1}{\frac{3}{2}} = 1 - \frac{2}{3} = \frac{3}{3} - \frac{2}{3} = \frac{1}{3}$$

д) $$1+\frac{1}{1+\frac{1}{1+\frac{1}{2}}} = 1+\frac{1}{1+\frac{1}{\frac{2}{2}+\frac{1}{2}}} = 1+\frac{1}{1+\frac{1}{\frac{3}{2}}} = 1+\frac{1}{1+\frac{2}{3}} = 1+\frac{1}{\frac{3}{3}+\frac{2}{3}} = 1+\frac{1}{\frac{5}{3}} = 1+\frac{3}{5} = \frac{5}{5}+\frac{3}{5} = \frac{8}{5} = 1\frac{3}{5}$$

г) $$2 + \frac{2}{1-\frac{2}{3}} = 2 + \frac{2}{\frac{3}{3} - \frac{2}{3}} = 2 + \frac{2}{\frac{1}{3}} = 2 + 2 \cdot 3 = 2 + 6 = 8$$

e) $$3-\frac{3}{3-\frac{1}{1-\frac{1}{3}}} = 3-\frac{3}{3-\frac{1}{\frac{3}{3}-\frac{1}{3}}} = 3-\frac{3}{3-\frac{1}{\frac{2}{3}}} = 3-\frac{3}{3-\frac{3}{2}} = 3-\frac{3}{\frac{6}{2}-\frac{3}{2}} = 3-\frac{3}{\frac{3}{2}} = 3 - 3 \cdot \frac{2}{3} = 3 - 2 = 1$$

Ответ: a) 6/35; б) 1/3; д) 8/5; г) 8; e) 1