a) \(\left(\frac{1}{4}:\frac{5}{12}+\frac{2}{3}\right):\frac{5}{4}\)

Решение:

1. \(\frac{1}{4}:\frac{5}{12} = \frac{1}{4} \times \frac{12}{5} = \frac{12}{20} = \frac{3}{5}\)
2. \(\frac{3}{5} + \frac{2}{3} = \frac{3 \times 3 + 2 \times 5}{15} = \frac{9+10}{15} = \frac{19}{15}\)
3. \(\frac{19}{15}:\frac{5}{4} = \frac{19}{15} \times \frac{4}{5} = \frac{76}{75}\)

Ответ: \(\frac{76}{75}\)