Ё) 8 · (3/4 + 4/57 − 2/3) + 4/36 + 15 · (5/8 − 3/47 − 2/3) − 31/55

Решение:

\( 8 \cdot (\frac{3}{4} + \frac{4}{57} - \frac{2}{3}) + \frac{4}{36} + 15 \cdot (\frac{5}{8} - \frac{3}{47} - \frac{2}{3}) - \frac{31}{55} \)

1. \( \frac{3}{4} + \frac{4}{57} - \frac{2}{3} = \frac{3 \cdot 57 + 4 \cdot 4 - 2 \cdot 76}{228} = \frac{171 + 16 - 152}{228} = \frac{35}{228} \)
2. \( 8 \cdot \frac{35}{228} = \frac{280}{228} = \frac{70}{57} \)
3. \( \frac{5}{8} - \frac{3}{47} - \frac{2}{3} = \frac{5 \cdot 47 \cdot 3 - 3 \cdot 8 \cdot 3 - 2 \cdot 8 \cdot 47}{8 \cdot 47 \cdot 3} = \frac{705 - 72 - 752}{1128} = \frac{-119}{1128} \)
4. \( 15 \cdot \frac{-119}{1128} = \frac{-1785}{1128} = \frac{-595}{376} \)
5. \( \frac{4}{36} = \frac{1}{9} \)
6. \( \frac{70}{57} + \frac{1}{9} + \frac{-595}{376} - \frac{31}{55} \)

Ответ: \( \frac{70}{57} + \frac{1}{9} - \frac{595}{376} - \frac{31}{55} \)