作业帮计算:(x^3+x^2y) / (x^2-y^3) - x(x-y)/ (xy+x^2)- (2xy)/(x^2-y^2)
来源：学生作业帮助网 编辑：作业帮 时间：2024/07/20 19:31:09
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计算:(x^3+x^2y) / (x^2-y^3) - x(x-y)/ (xy+x^2)- (2xy)/(x^2-y^2)
计算:(x^3+x^2y) / (x^2-y^3) - x(x-y)/ (xy+x^2)- (2xy)/(x^2-y^2)
计算:(x^3+x^2y) / (x^2-y^3) - x(x-y)/ (xy+x^2)- (2xy)/(x^2-y^2)
[(x^3+x^2y)/(x^2y-y^3)]-{[x(x-y)]/(xy+x^2)}-[(2xy)/(x^2-y^2)]
原式=[x^2(x+y)/y(x+y)(x-y))]-[x(x-y)]/[x(y+x)]-[2xy/(x+y)(x-y)]
=[x^2/y(x-y)]-(x-y)/(x+y)-2xy/(x+y)(x-y)
=[x^2(x+y)-y(x-y)^2-2xy^2]/y(x+y)(x-y)
=(x^3+x^2y-x^2y+2xy^2-y^3-2xy^2)/y(x+y)(x-y)
=(x^3-y^3)/y(x+y)(x-y)
=(x-y)(x^2+xy+y^2)/y(x+y)(x-y)
=(x^2+xy+y^2)/y(x+y)
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