2 Сравните А₁ = \(\frac{5}{6} + \frac{1}{3} + \frac{1}{9}\) и А2 = \(\frac{7}{9} + \frac{1}{2} + \frac{1}{3}\).

2. Сравним А₁ = \(\frac{5}{6} + \frac{1}{3} + \frac{1}{9}\) и А2 = \(\frac{7}{9} + \frac{1}{2} + \frac{1}{3}\).

1. \(A_1 = \frac{5}{6} + \frac{1}{3} + \frac{1}{9} = \frac{5 \cdot 3}{6 \cdot 3} + \frac{1 \cdot 6}{3 \cdot 6} + \frac{1 \cdot 2}{9 \cdot 2} = \frac{15}{18} + \frac{6}{18} + \frac{2}{18} = \frac{15+6+2}{18} = \frac{23}{18} = 1\frac{5}{18}\)
2. \(A_2 = \frac{7}{9} + \frac{1}{2} + \frac{1}{3} = \frac{7 \cdot 2}{9 \cdot 2} + \frac{1 \cdot 9}{2 \cdot 9} + \frac{1 \cdot 6}{3 \cdot 6} = \frac{14}{18} + \frac{9}{18} + \frac{6}{18} = \frac{14+9+6}{18} = \frac{29}{18} = 1\frac{11}{18}\)
3. Сравним \(A_1 = 1\frac{5}{18}\) и \(A_2 = 1\frac{11}{18}\). Очевидно, что \(A_1 < A_2\)

Ответ: \(A_1 < A_2\)