2. Вычислите: а) 55/48 : (11/16 + 3/32) - 14/15 ⋅ 5/7; б) (1/12 + 1/13)^2 : (1/12 - 1/13)^2 ⋅ (1/10)^3.

а) \[\frac{55}{48} : (\frac{11}{16} + \frac{3}{32}) - \frac{14}{15} \cdot \frac{5}{7} = \frac{55}{48} : (\frac{22}{32} + \frac{3}{32}) - \frac{14}{15} \cdot \frac{5}{7} = \frac{55}{48} : \frac{25}{32} - \frac{14 \cdot 5}{15 \cdot 7} = \frac{55}{48} \cdot \frac{32}{25} - \frac{2 \cdot 5}{3 \cdot 7} = \frac{11 \cdot 2}{3 \cdot 5} - \frac{2}{3} = \frac{22}{15} - \frac{2}{3} = \frac{22}{15} - \frac{10}{15} = \frac{12}{15} = \frac{4}{5}\]

б) \[(\frac{1}{12} + \frac{1}{13})^2 : (\frac{1}{12} - \frac{1}{13})^2 \cdot (\frac{1}{10})^3 = (\frac{13}{156} + \frac{12}{156})^2 : (\frac{13}{156} - \frac{12}{156})^2 \cdot \frac{1}{1000} = (\frac{25}{156})^2 : (\frac{1}{156})^2 \cdot \frac{1}{1000} = \frac{25^2}{156^2} : \frac{1}{156^2} \cdot \frac{1}{1000} = \frac{625}{156^2} \cdot \frac{156^2}{1} \cdot \frac{1}{1000} = \frac{625}{1000} = \frac{5}{8}\]