问题 解答题
先化简,再求值.(
2
x-2
-
x-2
x2-4x+4
x2+2x
x-2
,其中x2+2x-4=0.
答案

∵x2+2x-4=0,

∴x(x+2)=4,

(

2
x-2
-
x-2
x2-4x+4
x2+2x
x-2

=(

2
x-2
-
x-2
(x-2)2
)•
x-2
x(x-2)

=

2
x(x+2)
-
1
x(x+2)
=
1
x(x+2)

∴当x(x+2)=4时,原式=

1
x(x+2)
=
1
4

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