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

原式=

(x+y)2-(x-y)2
x2-y2
y2-x2
x2y2

=

x2+2xy+y2-x2+2xy+y2
(x+y)(x-y)
•(-
(x+y)(x-y)
x2y2

=4xy•

-1
x2y2

=-

4
xy

则当x=2+

3
,y=2-
3
时,原式=-
4
(2+
3
)(2-
3
)
=-
4
22-(
3
)
2
=-4.

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