1. Сократите дробь: 1) а) x(a+3)/(y(a+3)); б) 3(x+5)²/(x+5)²; в) 3a(b−2)/(6(b−2)²); г) x²(x−8)³/(x⁴(x−8)²). 2) а) (3a+3b)/(5(a+b)); б) (7x−14y)/(3x−6y); в) (5a−20c)/(15ac); г) (x−2b)/(x²−2bx). 3) а) 2(x−y)/(x(y−x)); б) (3c−9d)/(6d−2c); в) (a²−2ab)/(6b−3a); г) (π³−5π²n)/(5n³−mn²). 4) а) (5x−10)/(x²−4); б) (a²−9)/(15+5a); в) (x²−4x+4)/(3x−6); г) (b²+6b+9)/(b²−9).

Используем разложение на множители и сокращаем только общие ненулевые множители.

1. 1)
   1. \(\dfrac{x(a+3)}{y(a+3)}=\dfrac{x}{y}\).
   2. \(\dfrac{3(x+5)^2}{(x+5)^2}=3\).
   3. \(\dfrac{3a(b-2)}{6(b-2)^2}=\dfrac{a}{2(b-2)}\).
   4. \(\dfrac{x^2(x-8)^3}{x^4(x-8)^2}=\dfrac{x-8}{x^2}\).
2. 2)
   1. \(\dfrac{3a+3b}{5(a+b)}=\dfrac{3(a+b)}{5(a+b)}=\dfrac35\).
   2. \(\dfrac{7x-14y}{3x-6y}=\dfrac{7(x-2y)}{3(x-2y)}=\dfrac73\).
   3. \(\dfrac{5a-20c}{15ac}=\dfrac{5(a-4c)}{15ac}=\dfrac{a-4c}{3ac}\).
   4. \(\dfrac{x-2b}{x^2-2bx}=\dfrac{x-2b}{x(x-2b)}=\dfrac1x\).
3. 3)
   1. Так как \(y-x=-(x-y)\), то \(\dfrac{2(x-y)}{x(y-x)}=-\dfrac2x\).
   2. \(\dfrac{3c-9d}{6d-2c}=\dfrac{3(c-3d)}{2(3d-c)}=-\dfrac32\).
   3. \(\dfrac{a^2-2ab}{6b-3a}=\dfrac{a(a-2b)}{3(2b-a)}=-\dfrac a3\).
   4. \(\dfrac{\pi^3-5\pi^2n}{5n^3-mn^2}=\dfrac{\pi^2(\pi-5n)}{n^2(5n-m)}\).
4. 4)
   1. \(\dfrac{5x-10}{x^2-4}=\dfrac{5(x-2)}{(x-2)(x+2)}=\dfrac5{x+2}\).
   2. \(\dfrac{a^2-9}{15+5a}=\dfrac{(a-3)(a+3)}{5(a+3)}=\dfrac{a-3}{5}\).
   3. \(\dfrac{x^2-4x+4}{3x-6}=\dfrac{(x-2)^2}{3(x-2)}=\dfrac{x-2}{3}\).
   4. \(\dfrac{b^2+6b+9}{b^2-9}=\dfrac{(b+3)^2}{(b-3)(b+3)}=\dfrac{b+3}{b-3}\).

Ответ: 1) а) \(\frac{x}{y}\); б) \(3\); в) \(\frac{a}{2(b-2)}\); г) \(\frac{x-8}{x^2}\). 2) а) \(\frac35\); б) \(\frac73\); в) \(\frac{a-4c}{3ac}\); г) \(\frac1x\). 3) а) \(-\frac2x\); б) \(-\frac32\); в) \(-\frac a3\); г) \(\frac{\pi^2(\pi-5n)}{n^2(5n-m)}\). 4) а) \(\frac5{x+2}\); б) \(\frac{a-3}{5}\); в) \(\frac{x-2}{3}\); г) \(\frac{b+3}{b-3}\).