б) \((1-\frac{11}{17})\cdot(\frac{3}{4}+\frac{5}{12})+\frac{11}{18}\);

Найдем значение выражения:

1) \(1 - \frac{11}{17} = \frac{17}{17} - \frac{11}{17} = \frac{17-11}{17} = \frac{6}{17}\)

2) \(\frac{3}{4} + \frac{5}{12} = \frac{3 \cdot 3}{4 \cdot 3} + \frac{5}{12} = \frac{9}{12} + \frac{5}{12} = \frac{9+5}{12} = \frac{14}{12} = \frac{7}{6}\)

3) \(\frac{6}{17} \cdot \frac{7}{6} = \frac{6 \cdot 7}{17 \cdot 6} = \frac{7}{17}\)

4) \(\frac{7}{17} + \frac{11}{18} = \frac{7 \cdot 18}{17 \cdot 18} + \frac{11 \cdot 17}{18 \cdot 17} = \frac{126}{306} + \frac{187}{306} = \frac{126+187}{306} = \frac{313}{306} = 1 \frac{7}{306}\)

Ответ: \(1 \frac{7}{306}\)