问题 解答题
(1)解分式方程:
x-2
2x-1
+1=
1.5
1-2x

(2)先化简,再求值:(
1
x+1
+
x2-2x+1
x2-1
x-1
x+1
,其中x=2.
答案

(1)方程变形得:

x-2
2x-1
+1=-
1.5
2x-1

去分母得:x-2+2x-1=-1.5,

解得:x=0.5,

经检验x=0.5是增根,原分式方程无解;

(2)原式=[

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

当x=2时,原式=

2
2-1
=2.

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