P) 3\(\frac{1}{8}\):[\(\frac{5}{12}-2\frac{13}{24}\)\(\cdot\)\(\frac{4}{7}\)+\(\frac{1}{18}-2\frac{7}{12}\)\(\cdot\)\(\frac{10}{17}\)]

Решение:

Выражение в квадратных скобках:

1. \( 2\frac{13}{24} = \frac{61}{24} \)
2. \( \frac{5}{12} - \frac{61}{24} = \frac{10-61}{24} = -\frac{51}{24} = -\frac{17}{8} \)
3. \( -\frac{17}{8} \cdot \frac{4}{7} = -\frac{17\cdot4}{8\cdot7} = -\frac{17}{14} \)
4. \( 2\frac{7}{12} = \frac{31}{12} \)
5. \( \frac{1}{18} - \frac{31}{12} = \frac{1\cdot2 - 31\cdot3}{36} = \frac{2-93}{36} = -\frac{91}{36} \)
6. \( -\frac{91}{36} \cdot \frac{10}{17} = -\frac{91\cdot10}{36\cdot17} = -\frac{910}{612} = -\frac{455}{306} \)
7. \( -\frac{17}{14} - \frac{455}{306} = \frac{-17\cdot153 - 455\cdot7}{2142} = \frac{-2501 - 3185}{2142} = \frac{-5686}{2142} = -\frac{2843}{1071} \)

Основное вычисление:

1. \( 3\frac{1}{8} = \frac{25}{8} \)
2. \( \frac{25}{8} : (-\frac{2843}{1071}) = \frac{25}{8} \cdot (-\frac{1071}{2843}) = -\frac{26775}{22744} \)

Ответ: -\(\frac{26775}{22744}\)