计算[4/(x^2-y^2)+(x+y)/(xy^2-x^2y)]除[(x+2y)(x-y)/(x^2+2xy^2)分式计算_数学解答

计算[4/(x^2-y^2)+(x+y)/(xy^2-x^2y)]除[(x+2y)(x-y)/(x^2+2xy^2)
分式计算

人气：405 ℃　时间：2019-08-22 14:33:38

解答

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