55. Тип 13 № 10148: Вычислите \(\frac{5}{6} + \frac{10}{9} \cdot (3 - \frac{17}{21}) - \frac{11}{30}\)

Решение:

1. \(3 - \frac{17}{21} = \frac{3 \cdot 21 - 17}{21} = \frac{63 - 17}{21} = \frac{46}{21}\)
2. \(\frac{10}{9} \cdot \frac{46}{21} = \frac{10 \cdot 46}{9 \cdot 21} = \frac{460}{189}\)
3. \(\frac{5}{6} + \frac{460}{189} = \frac{5 \cdot 63 + 460 \cdot 2}{6 \cdot 63} = \frac{315 + 920}{378} = \frac{1235}{378}\)
4. \(\frac{1235}{378} - \frac{11}{30} = \frac{1235 \cdot 5 - 11 \cdot 63}{378 \cdot 5} = \frac{6175 - 693}{1890} = \frac{5482}{1890} = \frac{2741}{945}\)

Ответ: \(\frac{2741}{945}\)