\(\left\(4\frac{1}{6}:3\frac{1}{3}-\frac{1}{5}+\frac{5}{6}\right\)\(\cdot\)3

Решение:

1. \( 4\frac{1}{6} = \frac{25}{6} \)
2. \( 3\frac{1}{3} = \frac{10}{3} \)
3. \( \frac{25}{6} : \frac{10}{3} = \frac{25}{6} \cdot \frac{3}{10} = \frac{5 \cdot 1}{2 \cdot 2} = \frac{5}{4} \)
4. \( \frac{5}{4} - \frac{1}{5} = \frac{25 - 4}{20} = \frac{21}{20} \)
5. \( \frac{21}{20} + \frac{5}{6} = \frac{21 \cdot 3 + 5 \cdot 10}{60} = \frac{63 + 50}{60} = \frac{113}{60} \)
6. \( \frac{113}{60} \cdot 3 = \frac{113}{20} \)

Ответ: \(\frac{113}{20}\)