问题 解答题
先化简,再求值:
2
x+1
-
1
x2-1
÷
x
x2-2x+1
,其中x=5.
答案

2
x+1
-
1
x2-1
÷
x
x2-2x+1

=

2
x+1
-
1
(x+1)(x-1)
×
(x-1)2
x

=

2
x+1
-
x-1
x(x+1)
(3分)

=

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

=

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

=

x+1
x(x+1)

=

1
x
,(4分)

当x=5时,原式=

1
x
=
1
5
.(5分)

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