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;
(
x-1
x
-
x-2
x+1
2x2-x
x2+2x+1
,其中x满足x2-x-1=0.
答案

①原式=

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

=

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

=

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

=

x+1
x(x+1)

=

1
x

当x=5时,原式=

1
5

②原式=[

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

=

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

=

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

=

x+1
x2

当x2-x-1=0时,x2=x+1,

则原式=1.

单项选择题
单项选择题