问题 解答题
先化简,再求值:(
x+2
x2-2x
-
x-1
x2-4x+4
x2-16
x2+4x
,其中x=2+
3
答案

原式=[

x+2
x(x-2)
-
x-1
(x-2)2
x2-16
x2+4x

=[

x2-4
x(x-2)2
-
x2-x
x(x-2)2
x2-16
x2+4x

=

x-4
x(x-2)2
x(x+4)
(x+4)(x-4)

=

1
(x-2)2

x=2+

3
时,

原式=

1
(2+
3
-2)
2

=

1
3

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