Question

分解因式：4/（x^2-y^2）+(x+y)/（xy^2-x^2y)÷（x^2+xy-2y^2）/（x^2+2xy）

不好意思题目打错了，应该是：[4/（x^2-y^2）+(x+y)/（xy^2-x^2y)]÷（x^2+xy-2y^2）/（x^2y+2xy^2），答案是-1/x+y,求过程

Answer 1

原式=[4/(x-y)(x+y)+(x+y)/xy(y-x)]xy(x+2y)/(x+2y)(x-y)
=[4/(x-y)(x+y)+(x+y)/xy(y-x)]xy/(x-y)
=-(x+y)/(x-y)^2+4xy/(x-y)^2(x+y)
=[(x+y)^2-4xy]/-(x-y)^2(x+y)
=(x-y)^2/-(x-y)^2(x+y)
=-1/(x+y)

Answer 2

4/（x^2-y^2）+(x+y)/（xy^2-x^2y)÷（x^2+xy-2y^2）/（x^2+2xy）
=4/（x-y)(x+y)+(x+y)/xy(y-x)÷（x+2y)(x-y）/x（x+2y）
=4/（x-y)(x+y)+(x+y)/xy(y-x)×x/(x-y）
=4/（x-y)(x+y)-(x+y)/y(x-y）^2
=[4y(x-y）^2-(x+y)^2]/y(x+y)(x-y）^2

Answer 3

4/（x^2-y^2）+(x+y)/（xy^2-x^2y)÷（x^2+xy-2y^2）/（x^2+2xy）
=4/(x²-y²)+(x+y)/xy(y-x)÷(x+2y)(x-y)/x(x+2y)
=4/(x²-y²)+(x+y)/y(y-x)(x-y)
=4/(x-y)(x+y)-(x+y)/y(x-y)²
=[4y(x-y)-(x+y)²]/y(x+y)(x-y)²
=(4xy-4y²-x²-2xy-y²)/y(x+y)(x-y)²
=(2xy-5y²-x²)/y(x+y)(x-y)²