Выполните вычитание или сложение дробей: 2x-1 x+2 3 6 4y-3 y+2 6y 4y 10b+3 b+2 18b 12b 4a 3a 3a-6 8-4a 3 3 x+7 x-7 7a+5 a-2 15a 6d a a² a+5 a²-25 3x+2 5x+3y y-1 5x 10xy 2y

Решения:

1) $$rac{2x-1}{3} - \frac{x+2}{6} = \frac{2(2x-1) - (x+2)}{6} = \frac{4x-2-x-2}{6} = \frac{3x-4}{6}$$

2) $$rac{4y-3}{6y} + \frac{y+2}{4y} = \frac{2(4y-3) + 3(y+2)}{12y} = \frac{8y-6+3y+6}{12y} = \frac{11y}{12y} = \frac{11}{12}$$

3) $$rac{10b+3}{18b} - \frac{b+2}{12b} = \frac{2(10b+3) - 3(b+2)}{36b} = \frac{20b+6-3b-6}{36b} = \frac{17b}{36b} = \frac{17}{36}$$

4) $$rac{4a}{3a-6} + \frac{3a}{8-4a} = \frac{4a}{3(a-2)} - \frac{3a}{4(a-2)} = \frac{16a - 9a}{12(a-2)} = \frac{7a}{12(a-2)}$$

5) $$rac{3}{x+7} - \frac{3}{x-7} = \frac{3(x-7) - 3(x+7)}{(x+7)(x-7)} = \frac{3x-21-3x-21}{x^2-49} = \frac{-42}{x^2-49}$$

6) $$rac{7a+5}{15a} + \frac{a-2}{6d} = \frac{2d(7a+5) + 5a(a-2)}{30ad} = \frac{14ad+10d+5a^2-10a}{30ad}$$

7) $$rac{a}{a+5} - \frac{a^2}{a^2-25} = \frac{a(a-5) - a^2}{(a+5)(a-5)} = \frac{a^2 - 5a - a^2}{a^2-25} = \frac{-5a}{a^2-25}$$

8) $$\frac{3x+2}{5x} - \frac{5x+3y}{10xy} - \frac{y-1}{2y} = \frac{2y(3x+2) - (5x+3y) - 5x(y-1)}{10xy} = \frac{6xy+4y-5x-3y-5xy+5x}{10xy} = \frac{xy+y}{10xy} = \frac{y(x+1)}{10xy} = \frac{x+1}{10x}$$