A) $$(\frac{5}{7} \times 2\frac{1}{3} \times \frac{5}{6} - 1) : (1 - \frac{7}{8} \times 1\frac{3}{5} \times \frac{3}{14})$$

Решим пример по действиям.

1. $$\frac{5}{7} \times 2\frac{1}{3} \times \frac{5}{6} = \frac{5}{7} \times \frac{7}{3} \times \frac{5}{6} = \frac{5 \times 7 \times 5}{7 \times 3 \times 6} = \frac{5 \times 5}{3 \times 6} = \frac{25}{18}$$
2. $$\frac{25}{18} - 1 = \frac{25}{18} - \frac{18}{18} = \frac{25-18}{18} = \frac{7}{18}$$
3. $$\frac{7}{8} \times 1\frac{3}{5} \times \frac{3}{14} = \frac{7}{8} \times \frac{8}{5} \times \frac{3}{14} = \frac{7 \times 8 \times 3}{8 \times 5 \times 14} = \frac{7 \times 8 \times 3}{8 \times 5 \times 7 \times 2} = \frac{3}{5 \times 2} = \frac{3}{10}$$
4. $$1 - \frac{3}{10} = \frac{10}{10} - \frac{3}{10} = \frac{10-3}{10} = \frac{7}{10}$$
5. $$\frac{7}{18} : \frac{7}{10} = \frac{7}{18} \times \frac{10}{7} = \frac{7 \times 10}{18 \times 7} = \frac{10}{18} = \frac{5}{9}$$

Ответ: $$\frac{5}{9}$$