Решение:

1. a) $$rac{\frac{1}{2} + \frac{1}{3}}{\frac{1}{2} - \frac{1}{3}} = \frac{\frac{3}{6} + \frac{2}{6}}{\frac{3}{6} - \frac{2}{6}} = \frac{\frac{5}{6}}{\frac{1}{6}} = \frac{5}{6} \cdot \frac{6}{1} = 5$$

   Ответ: 5

2. б) $$rac{\frac{1}{3} - \frac{1}{5}}{\frac{2}{5} + \frac{2}{3}} = \frac{\frac{5}{15} - \frac{3}{15}}{\frac{6}{15} + \frac{10}{15}} = \frac{\frac{2}{15}}{\frac{16}{15}} = \frac{2}{15} \cdot \frac{15}{16} = \frac{2}{16} = \frac{1}{8}$$

   Ответ: $$\frac{1}{8}$$

3. в) $$1\frac{1}{2} - 7\frac{5}{8} = \frac{3}{2} - \frac{61}{8} = \frac{12}{8} - \frac{61}{8} = -\frac{49}{8} = -6\frac{1}{8}$$

   Ответ: $$-6\frac{1}{8}$$

4. г) $$2\frac{1}{3} - 5\frac{1}{9} = \frac{7}{3} - \frac{46}{9} = \frac{21}{9} - \frac{46}{9} = -\frac{25}{9} = -2\frac{7}{9}$$

   Ответ: $$-2\frac{7}{9}$$

5. д) $$2\frac{1}{2} + 3\frac{1}{3} = \frac{5}{2} + \frac{10}{3} = \frac{15}{6} + \frac{20}{6} = \frac{35}{6} = 5\frac{5}{6}$$

   Ответ: $$5\frac{5}{6}$$

6. е) $$1\frac{1}{2} : 1\frac{1}{3} = \frac{3}{2} : \frac{4}{3} = \frac{3}{2} \cdot \frac{3}{4} = \frac{9}{8} = 1\frac{1}{8}$$

   Ответ: $$1\frac{1}{8}$$