B) $$(1\frac{8}{13} \times \frac{13}{42} + 5\frac{5}{7} : \frac{8}{21}) : (8\frac{1}{8} + 2\frac{1}{2})$$

Решим пример по действиям.

1. Преобразуем смешанные дроби в неправильные:
   • $$1\frac{8}{13} = \frac{1 \times 13 + 8}{13} = \frac{13 + 8}{13} = \frac{21}{13}$$
   • $$5\frac{5}{7} = \frac{5 \times 7 + 5}{7} = \frac{35 + 5}{7} = \frac{40}{7}$$
   • $$8\frac{1}{8} = \frac{8 \times 8 + 1}{8} = \frac{64 + 1}{8} = \frac{65}{8}$$
   • $$2\frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{4 + 1}{2} = \frac{5}{2}$$
2. $$\frac{21}{13} \times \frac{13}{42} = \frac{21 \times 13}{13 \times 42} = \frac{21}{42} = \frac{1}{2}$$
3. $$\frac{40}{7} : \frac{8}{21} = \frac{40}{7} \times \frac{21}{8} = \frac{40 \times 21}{7 \times 8} = \frac{40 \times 3}{8} = 5 \times 3 = 15$$
4. $$\frac{1}{2} + 15 = \frac{1}{2} + \frac{30}{2} = \frac{1 + 30}{2} = \frac{31}{2}$$
5. $$\frac{65}{8} + \frac{5}{2} = \frac{65}{8} + \frac{5 \times 4}{2 \times 4} = \frac{65}{8} + \frac{20}{8} = \frac{65 + 20}{8} = \frac{85}{8}$$
6. $$\frac{31}{2} : \frac{85}{8} = \frac{31}{2} \times \frac{8}{85} = \frac{31 \times 8}{2 \times 85} = \frac{31 \times 4}{85} = \frac{124}{85} = 1\frac{39}{85}$$

Ответ: $$1\frac{39}{85}$$