问题 解答题
(1)先化简,再求值:(1-
1
x
)
÷
x2-2x+1
x2-1
,其中x=2.
(2)解方程:
x
x-1
 -1=
3
(x-1)(x+2)
答案

(1)原式=

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

当x=2时,原式=

2+1
2
=
3
2

(2)方程的两边同乘(x-1)(x+2),得

x(x+2)-(x-1)(x+2)=3,

x2+2x-x2-x+2=3,

解得x=1.

检验:把x=-1代入(x-1)(x+2)=0.

∴原方程无解.

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