问题 解答题
先化简再求值(1-
2x
x+y
x2-2xy+y2
3x+3y
+
x2+xy
x2-xy
,其中x=
2
+1,y=2
2
答案

原式=

x+y-2x
x+y
÷
(x-y)2
3(x+y)
+
x(x+y)
x(x-y)
=
y-x
x+y
3(x+y)
(y-x)2
+
x+y
x-y
=-
3
x-y
+
x+y
x-y
=
x+y-3
x-y

当x=

2
+1,y=2
2
时,

原式=

2
+1+2
2
-3
2
+1-2
2
=
3
2
-2
1-
2

=-(3

2
-2)(1+
2

=-(3

2
+6-2-2
2

=-

2
-4.

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