Ч) \( \frac{\left( 8\frac{1}{4} - \frac{3}{4} \right) : 3\frac{1}{2} + \frac{\left( 3\frac{1}{8} - 1\frac{7}{8} \right) \cdot 1\frac{3}{5}}{\left( 5-4\frac{2}{5} \right) : 10}}{\left( 2-1\frac{3}{8} \right)} \)

Решение:

Числитель:

1. \( 8\frac{1}{4} - \frac{3}{4} = 7\frac{5}{4} - \frac{3}{4} = 7\frac{2}{4} = 7\frac{1}{2} = \frac{15}{2} \)
2. \( \frac{15}{2} : 3\frac{1}{2} = \frac{15}{2} : \frac{7}{2} = \frac{15}{2} \cdot \frac{2}{7} = \frac{15}{7} \)
3. \( 3\frac{1}{8} - 1\frac{7}{8} = 2\frac{9}{8} - 1\frac{7}{8} = 1\frac{2}{8} = 1\frac{1}{4} = \frac{5}{4} \)
4. \( \frac{5}{4} \cdot 1\frac{3}{5} = \frac{5}{4} \cdot \frac{8}{5} = 2 \)
5. \( 5 - 4\frac{2}{5} = \frac{25}{5} - \frac{22}{5} = \frac{3}{5} \)
6. \( \frac{3}{5} : 10 = \frac{3}{50} \)
7. \( \frac{15}{7} + \frac{2}{\frac{3}{50}} = \frac{15}{7} + 2 \cdot \frac{50}{3} = \frac{15}{7} + \frac{100}{3} = \frac{15 \cdot 3 + 100 \cdot 7}{21} = \frac{45 + 700}{21} = \frac{745}{21} \)

Знаменатель:

1. \( 2 - 1\frac{3}{8} = 1 - \frac{3}{8} = \frac{5}{8} \)

Деление числителя на знаменатель:

1. \( \frac{745}{21} : \frac{5}{8} = \frac{745}{21} \cdot \frac{8}{5} = \frac{149 \cdot 8}{21} = \frac{1192}{21} \)

Ответ: \( \frac{1192}{21} \)