4). \( (3 \frac{1}{4} + 3 \frac{5}{6}) : (5 \frac{3}{4} - 3 \frac{2}{3}) \)

Решение:

1. \( 3 \frac{1}{4} = \frac{13}{4} \)
2. \( 3 \frac{5}{6} = \frac{23}{6} \)
3. \( \frac{13}{4} + \frac{23}{6} = \frac{13 \cdot 3}{4 \cdot 3} + \frac{23 \cdot 2}{6 \cdot 2} = \frac{39}{12} + \frac{46}{12} = \frac{85}{12} \)
4. \( 5 \frac{3}{4} = \frac{23}{4} \)
5. \( 3 \frac{2}{3} = \frac{11}{3} \)
6. \( \frac{23}{4} - \frac{11}{3} = \frac{23 \cdot 3}{4 \cdot 3} - \frac{11 \cdot 4}{3 \cdot 4} = \frac{69}{12} - \frac{44}{12} = \frac{25}{12} \)
7. \( \frac{85}{12} : \frac{25}{12} = \frac{85}{12} \cdot \frac{12}{25} = \frac{85}{25} = \frac{17}{5} = 3 \frac{2}{5} \)

Ответ: \( 3 \frac{2}{5} \)