(2$$\frac{5}{14}\cdot4\frac{2}{3}+12:2\frac{1}{4}-15\frac{1}{4}):(4\frac{7}{18}-2\frac{5}{9})

Решим выражение по действиям:

1. $$2\frac{5}{14}\cdot4\frac{2}{3} = \frac{33}{14} \cdot \frac{14}{3} = \frac{33 \cdot 14}{14 \cdot 3} = \frac{33}{3} = 11$$
2. $$12 : 2\frac{1}{4} = 12 : \frac{9}{4} = 12 \cdot \frac{4}{9} = \frac{12 \cdot 4}{9} = \frac{48}{9} = \frac{16}{3} = 5\frac{1}{3}$$
3. $$15\frac{1}{4} = \frac{61}{4}$$
4. $$11 + 5\frac{1}{3} - 15\frac{1}{4} = 11 + \frac{16}{3} - \frac{61}{4} = \frac{11 \cdot 12}{12} + \frac{16 \cdot 4}{3 \cdot 4} - \frac{61 \cdot 3}{4 \cdot 3} = \frac{132}{12} + \frac{64}{12} - \frac{183}{12} = \frac{132 + 64 - 183}{12} = \frac{196 - 183}{12} = \frac{13}{12} = 1\frac{1}{12}$$
5. $$4\frac{7}{18} - 2\frac{5}{9} = 4\frac{7}{18} - 2\frac{10}{18} = 3\frac{25}{18} - 2\frac{10}{18} = 1\frac{15}{18} = 1\frac{5}{6} = \frac{11}{6}$$
6. $$1\frac{1}{12} : 1\frac{5}{6} = \frac{13}{12} : \frac{11}{6} = \frac{13}{12} \cdot \frac{6}{11} = \frac{13 \cdot 6}{12 \cdot 11} = \frac{13 \cdot 1}{2 \cdot 11} = \frac{13}{22}$$

Ответ: $$\frac{13}{22}$$