7) \(1\frac{17}{34} : \left(8\frac{1}{6}+2\frac{6}{24}\right)\)

1. \(1\frac{17}{34}=1\frac{1}{2}\), \(2\frac{6}{24}=2\frac{1}{4}\).
2. \(8\frac{1}{6}+2\frac{1}{4}=10+\frac{2}{12}+\frac{3}{12}=10\frac{5}{12}=\frac{125}{12}\).
3. \(1\frac{1}{2}:\frac{125}{12}=\frac{3}{2}\cdot\frac{12}{125}=\frac{18}{125}\).

Ответ: \(\frac{18}{125}\).