9. 2 6/7 : (5/6 - 9/14) =

9. $$2 \frac{6}{7} : (\frac{5}{6} - \frac{9}{14}) = \frac{20}{7} : (\frac{5^{(7}}{6} - \frac{9^{(3}}{14}) = \frac{20}{7} : (\frac{35}{42} - \frac{27}{42}) = \frac{20}{7} : \frac{35 - 27}{42} = \frac{20}{7} : \frac{8}{42} = \frac{20}{7} \cdot \frac{42}{8} = \frac{20 \cdot 42}{7 \cdot 8} = \frac{5 \cdot 6}{1 \cdot 2} = 5 \cdot 3 = 15$$

Ответ: 15