Сократите дроби: а) (3y + 9)/(y² − 9); б) (b² − 4)/(6 + 3b); в) (a² + 10a + 25)/(3a + 15); г) (x² − 9)/(3x² + x³); д) (x² − 8x + 16)/(16 − x²); е) (y³ + 27)/(y² − 3y + 9).

1. \(\dfrac{3y+9}{y^2-9}=\dfrac{3(y+3)}{(y-3)(y+3)}=\dfrac{3}{y-3}\), \(y\ne\pm3\).
2. \(\dfrac{b^2-4}{6+3b}=\dfrac{(b-2)(b+2)}{3(b+2)}=\dfrac{b-2}{3}\), \(b\ne-2\).
3. \(\dfrac{a^2+10a+25}{3a+15}=\dfrac{(a+5)^2}{3(a+5)}=\dfrac{a+5}{3}\), \(a\ne-5\).
4. \(\dfrac{x^2-9}{3x^2+x^3}=\dfrac{(x-3)(x+3)}{x^2(x+3)}=\dfrac{x-3}{x^2}\), \(x\ne0,-3\).
5. \(\dfrac{x^2-8x+16}{16-x^2}=\dfrac{(x-4)^2}{(4-x)(4+x)}=\dfrac{(x-4)^2}{-(x-4)(x+4)}=\dfrac{4-x}{x+4}\), \(x\ne\pm4\).
6. \(\dfrac{y^3+27}{y^2-3y+9}=\dfrac{(y+3)(y^2-3y+9)}{y^2-3y+9}=y+3\).

Ответ: а) \(\dfrac{3}{y-3}\); б) \(\dfrac{b-2}{3}\); в) \(\dfrac{a+5}{3}\); г) \(\dfrac{x-3}{x^2}\); д) \(\dfrac{4-x}{x+4}\); е) \(y+3\).