55. Вычислите: \(\frac{5}{6}+\frac{10}{9}:(3-1\frac{17}{21})-1\frac{11}{30}\).

\(1\frac{17}{21}=\frac{80}{21}\), поэтому \(3-1\frac{17}{21}=\frac{63}{21}-\frac{80}{21}=-\frac{17}{21}\).

\[\frac{5}{6}+\frac{10}{9}:\left(-\frac{17}{21}\right)-1\frac{11}{30}=\frac{5}{6}-\frac{10}{9}\cdot\frac{21}{17}-\frac{41}{30}=\frac{5}{6}-\frac{70}{51}-\frac{41}{30}.\]

Приведём к общему знаменателю \(510\):

\[\frac{425}{510}-\frac{700}{510}-\frac{697}{510}=-\frac{972}{510}=-\frac{162}{85}=-1\frac{77}{85}.\]

Ответ: \(-1\frac{77}{85}\).