30. Сократите дробь: а) (y² − 16)/(3y + 12); б) (5x − 15y)/(x² − 9y²); в) (c + 2)²/(7c² + 14c); г) (6cd − 18c)/(d − 3)²; д) (a² + 10a + 25)/(a² − 25); е) (y² − 9)/(y² − 6y + 9).

1. Разложим на множители: \(y^2-16=(y-4)(y+4)\), \(3y+12=3(y+4)\).
   \(\dfrac{y^2-16}{3y+12}=\dfrac{(y-4)(y+4)}{3(y+4)}=\dfrac{y-4}{3}\).
2. \(5x-15y=5(x-3y)\), \(x^2-9y^2=(x-3y)(x+3y)\).
   \(\dfrac{5x-15y}{x^2-9y^2}=\dfrac{5(x-3y)}{(x-3y)(x+3y)}=\dfrac5{x+3y}\).
3. \(7c^2+14c=7c(c+2)\).
   \(\dfrac{(c+2)^2}{7c^2+14c}=\dfrac{(c+2)^2}{7c(c+2)}=\dfrac{c+2}{7c}\).
4. \(6cd-18c=6c(d-3)\).
   \(\dfrac{6cd-18c}{(d-3)^2}=\dfrac{6c(d-3)}{(d-3)^2}=\dfrac{6c}{d-3}\).
5. \(a^2+10a+25=(a+5)^2\), \(a^2-25=(a-5)(a+5)\).
   \(\dfrac{a^2+10a+25}{a^2-25}=\dfrac{(a+5)^2}{(a-5)(a+5)}=\dfrac{a+5}{a-5}\).
6. \(y^2-9=(y-3)(y+3)\), \(y^2-6y+9=(y-3)^2\).
   \(\dfrac{y^2-9}{y^2-6y+9}=\dfrac{(y-3)(y+3)}{(y-3)^2}=\dfrac{y+3}{y-3}\).

Ответ: а) \(\dfrac{y-4}{3}\); б) \(\dfrac5{x+3y}\); в) \(\dfrac{c+2}{7c}\); г) \(\dfrac{6c}{d-3}\); д) \(\dfrac{a+5}{a-5}\); е) \(\dfrac{y+3}{y-3}\).