С) 2\(\frac{3}{4}\):[(\(\frac{5}{7}-1\frac{11}{14}\))\(\cdot\)\(\frac{2}{3}\)+\(\frac{2}{9}-1\frac{5}{6}\)\(\cdot\)\(\frac{18}{25}\)]

Решение:

Выражение в квадратных скобках:

1. \( 1\frac{11}{14} = \frac{25}{14} \)
2. \( \frac{5}{7} - \frac{25}{14} = \frac{10-25}{14} = -\frac{15}{14} \)
3. \( -\frac{15}{14} \cdot \frac{2}{3} = -\frac{15\cdot2}{14\cdot3} = -\frac{30}{42} = -\frac{5}{7} \)
4. \( 1\frac{5}{6} = \frac{11}{6} \)
5. \( \frac{2}{9} - \frac{11}{6} = \frac{2\cdot2 - 11\cdot3}{18} = \frac{4-33}{18} = -\frac{29}{18} \)
6. \( -\frac{29}{18} \cdot \frac{18}{25} = -\frac{29\cdot18}{18\cdot25} = -\frac{29}{25} \)
7. \( -\frac{5}{7} - \frac{29}{25} = \frac{-5\cdot25 - 29\cdot7}{175} = \frac{-125 - 203}{175} = -\frac{328}{175} \)

Основное вычисление:

1. \( 2\frac{3}{4} = \frac{11}{4} \)
2. \( \frac{11}{4} : (-\frac{328}{175}) = \frac{11}{4} \cdot (-\frac{175}{328}) = -\frac{11\cdot175}{4\cdot328} = -\frac{1925}{1312} \)

Ответ: -\(\frac{1925}{1312}\)