31. Вычислите: \(4:\frac{16}{19}+3\frac{3}{5}\cdot\left(\frac{5}{12}-3\frac{13}{24}\right)\).

\[4:\frac{16}{19}=4\cdot\frac{19}{16}=\frac{19}{4}.\]

\[\frac{5}{12}-3\frac{13}{24}=\frac{10}{24}-\frac{85}{24}=-\frac{75}{24}=-\frac{25}{8}.\]

\[3\frac{3}{5}\cdot\left(-\frac{25}{8}\right)=\frac{18}{5}\cdot\left(-\frac{25}{8}\right)=-\frac{45}{4}.\]

\[\frac{19}{4}-\frac{45}{4}=-\frac{13}{2}.\]

Ответ: \(-\frac{13}{2}\).