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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

分类: 作业答案 • 2021-12-20 01:27:58
问题描述：

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

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)

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