分解因式：[4/（x^2-y^2）+(x+y)/（xy^2-x^2y)]÷（x^2+xy-2y^2）/（x^2y+2xy^2）
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^2y+2xy^2）
答
=[4/(x+y)(x-y)-(x+y)/xy(x-y)]÷(x+2y)(x-y)/xy(x+y)=(4xy-x²-2xy-y²)/xy(x+y)(x-y)×xy(x+y)/(x+2y)(x-y)=-(x-y)²/(x-y)×1/(x+2y)(x-y)=-1/(x+2y)