Вычислите: \(\frac{17}{12}:3\frac{2}{5}-\frac{2}{5}\cdot\left(2-1\frac{1}{12}\right)\).

Преобразуем смешанные числа в неправильные дроби:

\[3\frac{2}{5}=\frac{17}{5},\qquad 1\frac{1}{12}=\frac{13}{12}.\]

Тогда

\[\frac{17}{12}:\frac{17}{5}-\frac{2}{5}\cdot\left(2-\frac{13}{12}\right)=\frac{17}{12}\cdot\frac{5}{17}-\frac{2}{5}\cdot\frac{11}{12}.\]

\[=\frac{5}{12}-\frac{22}{60}=\frac{5}{12}-\frac{11}{30}=\frac{25}{60}-\frac{22}{60}=\frac{3}{60}=\frac{1}{20}.\]

Ответ: \(\frac{1}{20}\).