问题 解答题
先化简,再求值:(
x+1
x-2
-
x-2
x-1
4x2-5x
x2-4
-
1
x-1
,其中x满足2x2-2x-7=0.
答案

原式=

(x+1)(x-1)-(x-2)2
(x-2)(x-1)
(x+2)(x-2)
x(4x-5)
-
1
x-1

=

4x-5
x-1
x+2
x(4x-5)
-
1
x-1

=

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

=

2
x2-x

∵2x2-2x-7=0,

x2-x=

7
2

∴原式=

4
7

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