先化简再求值:(x-y-x2x+y)÷(2y2x2+2xy+y2)+x2-y2x-y,其中x≠y且x,y满足(x-y)(x+y-12)=0.-数学

题目简介

先化简再求值:(x-y-x2x+y)÷(2y2x2+2xy+y2)+x2-y2x-y,其中x≠y且x,y满足(x-y)(x+y-12)=0.-数学

题目详情

先化简再求值:(x-y-
x2
x+y
)÷(
2y2
x2+2xy+y2
)+
x2-y2
x-y
,其中x≠y且x,y满足(x-y)(x+y-12)=0.
题型:解答题难度:中档来源:不详

答案

原式=[
(x-y)(x+y)
x+y
-
x2
x+y
2y2
(x-y)2
+
(x+y)(x-y)
x-y
=
-y2
x+y
(x+y)2
2y2
+x+y
=-class="stub"x+y
2
+x+y
=class="stub"x+y
2

∵x≠y,且(x-y)(x+y+2)=0
∴x+y-12=0
∴x+y=12
∴原式=6

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