Сократите дробь: а) \(\frac{(2a-2b)^2}{a-b}\); б) \(\frac{(3c+9d)^2}{c+3d}\); в) \(\frac{(3x+6y)^2}{5x+10y}\); г) \(\frac{4x^2-y^2}{(10x+5y)^2}\).

1. а) \(\frac{(2a-2b)^2}{a-b}=\frac{[2(a-b)]^2}{a-b}=\frac{4(a-b)^2}{a-b}=4(a-b)\), при \(a\ne b\).
2. б) \(\frac{(3c+9d)^2}{c+3d}=\frac{[3(c+3d)]^2}{c+3d}=\frac{9(c+3d)^2}{c+3d}=9(c+3d)\), при \(c+3d\ne0\).
3. в) \(\frac{(3x+6y)^2}{5x+10y}=\frac{[3(x+2y)]^2}{5(x+2y)}=\frac{9(x+2y)^2}{5(x+2y)}=\frac{9(x+2y)}{5}\), при \(x+2y\ne0\).
4. г) \(\frac{4x^2-y^2}{(10x+5y)^2}=\frac{(2x-y)(2x+y)}{[5(2x+y)]^2}=\frac{(2x-y)(2x+y)}{25(2x+y)^2}=\frac{2x-y}{25(2x+y)}\), при \(2x+y\ne0\).

Ответ: а) \(4(a-b)\); б) \(9(c+3d)\); в) \(\frac{9(x+2y)}{5}\); г) \(\frac{2x-y}{25(2x+y)}\).