Сократите дробь: а) \(\dfrac{(x-y)^2}{x(x^2-2xy+y^2)}\); б) \(\dfrac{xc-3yc}{x^2-9y^2}\); в) \(\dfrac{14a^2(x-y)^2}{21a(x^2-y^2)}\); г) \(\dfrac{-ax-yx}{cy+ca}\); д) \(\dfrac{270xy^2}{360x^2y^2}\).

1. а) \(x^2-2xy+y^2=(x-y)^2\), поэтому \(\dfrac{(x-y)^2}{x(x-y)^2}=\dfrac1x\).
2. б) \(xc-3yc=c(x-3y)\), а \(x^2-9y^2=(x-3y)(x+3y)\). Поэтому \(\dfrac{c(x-3y)}{(x-3y)(x+3y)}=\dfrac{c}{x+3y}\).
3. в) \(x^2-y^2=(x-y)(x+y)\). Тогда \(\dfrac{14a^2(x-y)^2}{21a(x-y)(x+y)}=\dfrac{2a(x-y)}{3(x+y)}\).
4. г) \(-ax-yx=-x(a+y)\), а \(cy+ca=c(y+a)=c(a+y)\). Поэтому \(\dfrac{-x(a+y)}{c(a+y)}=-\dfrac{x}{c}\).
5. д) \(\dfrac{270xy^2}{360x^2y^2}=\dfrac{3}{4x}\).

Ответ: а) \(\dfrac1x\); б) \(\dfrac{c}{x+3y}\); в) \(\dfrac{2a(x-y)}{3(x+y)}\); г) \(-\dfrac{x}{c}\); д) \(\dfrac{3}{4x}\).