1) \(\left(\frac{9}{14}+\frac{17}{21}\right)\cdot9\)

Общий знаменатель дробей — 42: \(\frac{9}{14}=\frac{27}{42}\), \(\frac{17}{21}=\frac{34}{42}\).

\(\left(\frac{27}{42}+\frac{34}{42}\right)\cdot9=\frac{61}{42}\cdot9=\frac{183}{14}=13\frac{1}{14}\).

Ответ: \(\frac{183}{14}=13\frac{1}{14}\).