Вычислите: \(\left(1-\frac{11}{17}\right)\cdot\left(\frac{3}{4}-\frac{5}{12}+\frac{11}{18}\right)\).

\[1-\frac{11}{17}=\frac{6}{17}\]

\[\frac{3}{4}-\frac{5}{12}+\frac{11}{18}=\frac{27}{36}-\frac{15}{36}+\frac{22}{36}=\frac{34}{36}=\frac{17}{18}\]

\[\frac{6}{17}\cdot\frac{17}{18}=\frac{1}{3}\]

Ответ: \(\frac{1}{3}\).