Сократите дробь: а) \(\frac{x^2-4x+4}{x^2-2x}\); б) \(\frac{3y^2+24y}{y^2+16y+64}\); в) \(\frac{a^2+a+1}{a^3-1}\); г) \(\frac{b+2}{b^3+8}\).

1. \(\displaystyle \frac{x^2-4x+4}{x^2-2x}=\frac{(x-2)^2}{x(x-2)}=\frac{x-2}{x}\), \(x\ne0,2\).
2. \(\displaystyle \frac{3y^2+24y}{y^2+16y+64}=\frac{3y(y+8)}{(y+8)^2}=\frac{3y}{y+8}\), \(y\ne-8\).
3. \(\displaystyle \frac{a^2+a+1}{a^3-1}=\frac{a^2+a+1}{(a-1)(a^2+a+1)}=\frac1{a-1}\), \(a\ne1\).
4. \(\displaystyle \frac{b+2}{b^3+8}=\frac{b+2}{(b+2)(b^2-2b+4)}=\frac1{b^2-2b+4}\), \(b\ne-2\).

Ответ: а) \(\frac{x-2}{x}\); б) \(\frac{3y}{y+8}\); в) \(\frac1{a-1}\); г) \(\frac1{b^2-2b+4}\).