Question

先化简,再求值;(x^2y-x^3)\(x^2+2xy+y^2)÷x\(x-y)×(x+y)\(x^2-2xy+y^2)

Answer 1

(x^2y-x^3)/(x^2+2xy+y^2)÷x/(x-y)×(x+y)/(x^2-2xy+y^2)

=x^2(y-x)/(x+y)^2÷x/(x-y)×(x+y)/(x-y)^2

=x^2(y-x)/(x+y)^2×(x-y)/x×(x+y)/(x-y)^2

=x(y-x)/(x+y)×1/(x-y)

=-x(x-y)/(x+y)×1/(x-y)

=-x/(x+y)

=(-1/3)/(1/3-2/3)

=(-1/3)/(-1/3)

=1