9. Вычислите: \(5\frac{2}{3} : \left(\frac{12}{17}-\frac{31}{5}\right)+19\cdot1\frac{4}{5}\).

\[5\frac{2}{3}=\frac{17}{3},\qquad 1\frac{4}{5}=\frac{9}{5}.\]

\[\frac{12}{17}-\frac{31}{5}=\frac{60-527}{85}=-\frac{467}{85}.\]

\[\frac{17}{3}:\left(-\frac{467}{85}\right)=-\frac{1445}{1401},\qquad 19\cdot\frac{9}{5}=\frac{171}{5}.\]

\[-\frac{1445}{1401}+\frac{171}{5}=\frac{-7225+239571}{7005}=\frac{232346}{7005}.\]

Ответ: \(\frac{232346}{7005}\).