Найдите значение выражения \(9\frac{3}{5}\cdot2\frac{1}{2}-\left(2\frac{1}{8}-1\frac{5}{12}\right):\frac{1}{4}\).

\(9\frac{3}{5}=\frac{48}{5},\quad 2\frac{1}{2}=\frac{5}{2},\quad 2\frac{1}{8}=\frac{17}{8},\quad 1\frac{5}{12}=\frac{17}{12}.\)

\[\frac{48}{5}\cdot\frac{5}{2}-\left(\frac{17}{8}-\frac{17}{12}\right):\frac{1}{4}=24-\left(\frac{51}{24}-\frac{34}{24}\right)\cdot4.\]

\[24-\frac{17}{24}\cdot4=24-\frac{17}{6}=\frac{144}{6}-\frac{17}{6}=\frac{127}{6}=21\frac{1}{6}.\]

Ответ: \(21\frac{1}{6}\).