Примеры на сложение и вычитание рациональных дробей

1. $$\frac{3}{x} + \frac{5}{y} = \frac{3y + 5x}{xy}$$
2. $$\frac{1}{6m} - \frac{6m + n}{6mn} = \frac{n - (6m + n)}{6mn} = \frac{n - 6m - n}{6mn} = \frac{-6m}{6mn} = -\frac{1}{n}$$
3. $$\frac{7}{a} - \frac{4}{b} = \frac{7b - 4a}{ab}$$
4. $$\frac{1}{7y} + \frac{2y + x}{7xy} = \frac{x + 2y + x}{7xy} = \frac{2x + 2y}{7xy} = \frac{2(x + y)}{7xy}$$
5. $$\frac{10}{k} + \frac{3}{cd} = \frac{10cd + 3k}{kd}$$
6. $$\frac{4y}{5x} + \frac{5x}{4y} = \frac{16y^2 + 25x^2}{20xy}$$
7. $$\frac{5}{xy} - \frac{4}{y} = \frac{5 - 4x}{xy}$$
8. $$\frac{2y}{3x} - \frac{3x}{2y} = \frac{4y^2 - 9x^2}{6xy}$$
9. $$\frac{7}{5ab} - \frac{8}{15ab} = \frac{21 - 8}{15ab} = \frac{13}{15ab}$$
10. $$\frac{1}{9a} - \frac{81a^2 - 4}{18a} = \frac{2 - (81a^2 - 4)}{18a} = \frac{2 - 81a^2 + 4}{18a} = \frac{6 - 81a^2}{18a} = \frac{3(2 - 27a^2)}{18a} = \frac{2 - 27a^2}{6a}$$
11. $$\frac{3}{4cd} + \frac{7}{12cd} = \frac{9 + 7}{12cd} = \frac{16}{12cd} = \frac{4}{3cd}$$
12. $$\frac{1}{a} - \frac{a^2 - 25}{5a} = \frac{5 - (a^2 - 25)}{5a} = \frac{5 - a^2 + 25}{5a} = \frac{30 - a^2}{5a}$$
13. $$\frac{a}{4b} - \frac{4b}{a} = \frac{a^2 - 16b^2}{4ab}$$
14. $$\frac{5a}{9b} + \frac{5a - 9b^2}{b} = \frac{5a + 9(5a - 9b^2)}{9b} = \frac{5a + 45a - 81b^2}{9b} = \frac{50a - 81b^2}{9b}$$
15. $$\frac{1}{3b} - \frac{1}{a} = \frac{a - 3b}{3ab}$$
16. $$c + \frac{2d - c^2}{c} = \frac{c^2 + 2d - c^2}{c} = \frac{2d}{c}$$
17. $$\frac{9}{x} - \frac{9}{5x} = \frac{45 - 9}{5x} = \frac{36}{5x}$$
18. $$7m + \frac{8n - 7m^2}{m} = \frac{7m^2 + 8n - 7m^2}{m} = \frac{8n}{m}$$
19. $$\frac{1}{x} - \frac{2}{7x} = \frac{7 - 2}{7x} = \frac{5}{7x}$$
20. $$4x - \frac{2y + 4x^2}{x} = \frac{4x^2 - (2y + 4x^2)}{x} = \frac{4x^2 - 2y - 4x^2}{x} = \frac{-2y}{x}$$