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

Решим пример по действиям:

1) $$(\frac{1}{2} - \frac{3}{5}) = (\frac{5}{10} - \frac{6}{10}) = -\frac{1}{10}$$

2) $$4\frac{1}{6} \cdot (-\frac{1}{10}) = \frac{25}{6} \cdot (-\frac{1}{10}) = -\frac{25}{60} = -\frac{5}{12}$$

3) $$(\frac{3}{4} + \frac{5}{6}) = (\frac{9}{12} + \frac{10}{12}) = \frac{19}{12}$$

4) $$\frac{19}{12} \cdot 6 = \frac{19 \cdot 6}{12} = \frac{19}{2} = 9\frac{1}{2}$$

5) $$-\frac{5}{12} + 9\frac{1}{2} = -\frac{5}{12} + 9\frac{6}{12} = 9\frac{1}{12}$$

Ответ: $$9\frac{1}{12}$$