(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,

这种题就是通分~
x^2+y^2 x+y
--------------------- --- ------------------
x^2-y^2 2x-2y
2(x^2+y^2) (x+y)(x+y)
=--------------------- --- ------------------
2* (x^2-y^2) 2(x-y)(x+y)
化简可得
2(x^2+y^2) - x^2-y^2-2xy
=----------------------------
2* (x^2-y^2)
x^2+y^2-2xy
=----------------------------
2* (x-y) (x+y)
(x-y)^2
=----------------------------
2* (x-y) (x+y)
(x-y)
= ----------------------------
2* (x+y)
结果为
(x-y)
----------------------------
2* (x+y)

(x²+y²)/(x²-y²) - (x+y)/(2x-2y)（通分）公分母：2(x+y)(x-y)
=(x²+y²)/2(x+y)(x-y) - (x+y)(x+y) /2(x+y)(x-y)
=(2x²+2y²-x²-2xy-y²)/2(x+y)(x-y)
=(x²+y²-2xy)/2(x+y)(x-y)
=(x-y)²/2(x+y)(x-y)
=(x-y)/(2x+zy)

你算得不对
(x^2+y^2)/(x^2-y^2) - (x+y)/(2x-2y)
原式=2(x^2+y^2)/2(x^2-y^2) - (x+y)²/2(x²-y²)
=﹙2x^2+2y^2-X²-2XY-Y²﹚/2(x^2-y^2)
=﹙X-Y﹚²／2﹙X²-Y²﹚
=﹙X-Y﹚／﹙2X+2Y﹚

应该是(x-y)/(2x+2y)

(x^2+y^2)/(x^2-y^2) - (x+y)/(2x-2y)=2(x^2+y^2)/2(x^2-y^2)-(x+y)^2/2(x^2-y^2)=(x-y)^2/2(x^2-y^2)
=(x-y)/(2x+2y)

(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)-(x+y)^2]/[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)]

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-...

你真的算错了
大概通分时出现问题了
(x^2+y^2)/(x^2-y^2) 减去 (x+y)/(2x-2y)
=(x²+y²)/(x+y)(x-y)-(x+y)²/2(x+y)(x-y)
=(2x²+2y²-x²-2xy-y²)/2(x+y)(x-y)
=(x²+y²-2xy)/2(x+y)(x-y)
=(x-y)/2(x+y)