5) Упростите дроби: а) (x²−9)/(3x²+x³); б) (x²−8x+16)/(16−x²); в) (y³+27)/(y²−3y+9); г) (20+10a+5a²)/(a³−8).

а) \(\dfrac{x^2-9}{3x^2+x^3}=\dfrac{(x-3)(x+3)}{x^2(x+3)}=\dfrac{x-3}{x^2}\), при \(x\ne0,-3\).

б) \(\dfrac{x^2-8x+16}{16-x^2}=\dfrac{(x-4)^2}{(4-x)(4+x)}=\dfrac{-(x-4)}{x+4}=\dfrac{4-x}{x+4}\), при \(x\ne\pm4\).

в) \(\dfrac{y^3+27}{y^2-3y+9}=\dfrac{(y+3)(y^2-3y+9)}{y^2-3y+9}=y+3\).

г) \(\dfrac{20+10a+5a^2}{a^3-8}=\dfrac{5(a^2+2a+4)}{(a-2)(a^2+2a+4)}=\dfrac{5}{a-2}\), при \(a\ne2\).

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