Выполните сложение или вычитание дробей: 1) $$\frac{y-20}{4y} + \frac{5y-2}{y^2}$$ 2) $$\frac{1}{5c-d} - \frac{1}{5c+d}$$ 3) $$\frac{7}{a+5} - \frac{7a-3}{a^2+5a}$$ 4) $$\frac{b^2}{2b-10} + \frac{25}{10-2b}$$

1. $$\frac{y-20}{4y} + \frac{5y-2}{y^2} = \frac{y(y-20)}{4y^2} + \frac{4(5y-2)}{4y^2} = \frac{y^2-20y+20y-8}{4y^2} = \frac{y^2-8}{4y^2}$$
2. $$\frac{1}{5c-d} - \frac{1}{5c+d} = \frac{5c+d}{(5c-d)(5c+d)} - \frac{5c-d}{(5c-d)(5c+d)} = \frac{5c+d-5c+d}{(5c-d)(5c+d)} = \frac{2d}{25c^2-d^2}$$
3. $$\frac{7}{a+5} - \frac{7a-3}{a^2+5a} = \frac{7a}{a(a+5)} - \frac{7a-3}{a(a+5)} = \frac{7a-7a+3}{a(a+5)} = \frac{3}{a(a+5)}$$
4. $$\frac{b^2}{2b-10} + \frac{25}{10-2b} = \frac{b^2}{2(b-5)} - \frac{25}{2(b-5)} = \frac{b^2-25}{2(b-5)} = \frac{(b-5)(b+5)}{2(b-5)} = \frac{b+5}{2}$$

Ответ:

1. $$\frac{y^2-8}{4y^2}$$
2. $$\frac{2d}{25c^2-d^2}$$
3. $$\frac{3}{a(a+5)}$$
4. $$\frac{b+5}{2}$$