(x^2+y^2)/(x^2-y^2) 减去 (x+y)/(2x-2y) ,化简.

来源：学生作业帮编辑：拍题作业网作业帮分类：数学作业时间：2024/04/29 14:03:36

(x^2+y^2)/(x^2-y^2) 减去 (x+y)/(2x-2y) ,化简.
我算出来的是:x^2-2xy+y^2,和别人的不一样,

你将分母漏了
(x^2+y^2)/(x^2-y^2) - (x+y)/(2x-2y)
= (x^2+y^2)/(x-y)(x+y) - (x+y)/2(x-y)
= 2(x^2+y^2)/2(x-y)(x+y) - (x+y)^2/2(x-y)(x+y)
= [2(x^2+y^2) - (x+y)^2]/2(x-y)(x+y)
= [2x^2+2y^2 - (x^2+y^2+2xy)]/2(x-y)(x+y)
= [2x^2+2y^2 - x^2-y^2-2xy]/2(x-y)(x+y)
= ( x^2+y^2-2xy)/2(x-y)(x+y)
= ( x-y)^2/2(x-y)(x+y)
= ( x-y)/2(x+y)

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