1. Сократите дробь: 1) a) \(\frac{x(a+3)}{y(a+3)}\) ; б) \(\frac{3(x+5)^2}{(x+5)^3}\) ; в) \(\frac{3a(b-2)}{6(b-2)^2}\) ; г) \(\frac{x^2(x-8)^3}{x^4(x-8)^2}\) 2) a) \(\frac{3a+3b}{5(a+b)}\) ; б) \(\frac{7x-14y}{3x-6y}\) ; в) \(\frac{5a-20c}{15ac}\) ; г) \(\frac{x-2b}{x^2-2bx}\) 3) a) \(\frac{2(x-y)}{x(y-x)}\) ; б) \(\frac{3c-9d}{6d-2c}\) ; в) \(\frac{a^2-2ab}{6b-3a}\) ; г) \(\frac{m^3-5m^2n}{5n^3-mn^2}\) 4) a) \(\frac{5x-10}{x^2-4}\) ; б) \(\frac{a^2-9}{15+5a}\) ; в) \(\frac{x^2-4x+4}{3x-6}\) ; г) \(\frac{b^2+6b+9}{b^2-9}\)

Решение:

1. 1) а) \( \frac{x(a+3)}{y(a+3)} = \frac{x}{y} \)
2. 1) б) \( \frac{3(x+5)^2}{(x+5)^3} = \frac{3}{x+5} \)
3. 1) в) \( \frac{3a(b-2)}{6(b-2)^2} = \frac{3a}{6(b-2)} = \frac{a}{2(b-2)} \)
4. 1) г) \( \frac{x^2(x-8)^3}{x^4(x-8)^2} = \frac{x-8}{x^2} \)
5. 2) а) \( \frac{3a+3b}{5(a+b)} = \frac{3(a+b)}{5(a+b)} = \frac{3}{5} \)
6. 2) б) \( \frac{7x-14y}{3x-6y} = \frac{7(x-2y)}{3(x-2y)} = \frac{7}{3} \)
7. 2) в) \( \frac{5a-20c}{15ac} = \frac{5(a-4c)}{15ac} \)
8. 2) г) \( \frac{x-2b}{x^2-2bx} = \frac{x-2b}{x(x-2b)} = \frac{1}{x} \)
9. 3) а) \( \frac{2(x-y)}{x(y-x)} = \frac{2(x-y)}{-x(x-y)} = \frac{2}{-x} = -\frac{2}{x} \)
10. 3) б) \( \frac{3c-9d}{6d-2c} = \frac{3(c-3d)}{2(3d-c)} = \frac{3(c-3d)}{-2(c-3d)} = -\frac{3}{2} \)
11. 3) в) \( \frac{a^2-2ab}{6b-3a} = \frac{a(a-2b)}{3(2b-a)} = \frac{a(a-2b)}{-3(a-2b)} = -\frac{a}{3} \)
12. 3) г) \( \frac{m^3-5m^2n}{5n^3-mn^2} = \frac{m^2(m-5n)}{n^2(5n^2-m)} \)
13. 4) а) \( \frac{5x-10}{x^2-4} = \frac{5(x-2)}{(x-2)(x+2)} = \frac{5}{x+2} \)
14. 4) б) \( \frac{a^2-9}{15+5a} = \frac{(a-3)(a+3)}{5(3+a)} = \frac{a-3}{5} \)
15. 4) в) \( \frac{x^2-4x+4}{3x-6} = \frac{(x-2)^2}{3(x-2)} = \frac{x-2}{3} \)
16. 4) г) \( \frac{b^2+6b+9}{b^2-9} = \frac{(b+3)^2}{(b-3)(b+3)} = \frac{b+3}{b-3} \)