问题 填空题
已知1<x<2,x+
1
x-1
=7
,则
x-1
-
1
x-1
的值是______.
答案

∵(

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

=x+

1
x-1
-3,

又∵x+

1
x-1
=7,

∴(

x-1
-
1
x-1
2=4,

又∵1<x<2,

x-1
-
1
x-1
<0,

x-1
-
1
x-1
=-2.

故填:-2.

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