\(\frac{3}{4} : (\frac{5}{6} + \frac{1}{4}) = \frac{3}{4} : (\frac{10}{12} + \frac{3}{12}) = \frac{3}{4} : \frac{13}{12} = \frac{3}{4} \cdot \frac{12}{13} = \frac{3 \cdot 12}{4 \cdot 13} = \frac{3 \cdot 3}{1 \cdot 13} = \frac{9}{13}\)
Ответ: \(\frac{9}{13}\).