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