2. 3\(\frac{1}{78}\): (x - 4\(\frac{7}{24}\)) = \(\frac{17}{18}\) + 1\(\frac{5}{6}\)

2. \(3\frac{1}{78}: (x - 4\frac{7}{24}) = \frac{17}{18} + 1\frac{5}{6}\) \(\frac{3 \cdot 78 + 1}{78} : (x - \frac{4 \cdot 24 + 7}{24}) = \frac{17}{18} + \frac{1 \cdot 6 + 5}{6}\) \(\frac{235}{78} : (x - \frac{103}{24}) = \frac{17}{18} + \frac{11}{6}\) \(\frac{235}{78} : (x - \frac{103}{24}) = \frac{17}{18} + \frac{11 \cdot 3}{6 \cdot 3}\) \(\frac{235}{78} : (x - \frac{103}{24}) = \frac{17}{18} + \frac{33}{18}\) \(\frac{235}{78} : (x - \frac{103}{24}) = \frac{50}{18}\) \(\frac{235}{78} : (x - \frac{103}{24}) = \frac{25}{9}\) \(x - \frac{103}{24} = \frac{235}{78} : \frac{25}{9}\) \(x - \frac{103}{24} = \frac{235}{78} \cdot \frac{9}{25}\) \(x - \frac{103}{24} = \frac{5 \cdot 47}{2 \cdot 3 \cdot 13} \cdot \frac{3 \cdot 3}{5 \cdot 5}\) \(x - \frac{103}{24} = \frac{47 \cdot 3}{2 \cdot 13 \cdot 5}\) \(x - \frac{103}{24} = \frac{141}{130}\) \(x = \frac{141}{130} + \frac{103}{24}\) \(x = \frac{141 \cdot 12}{130 \cdot 12} + \frac{103 \cdot 65}{24 \cdot 65}\) \(x = \frac{1692}{1560} + \frac{6695}{1560}\) \(x = \frac{1692 + 6695}{1560}\) \(x = \frac{8387}{1560}\) \(x = 5\frac{587}{1560}\)

Ответ: \(5\frac{587}{1560}\)