问题 解答题
(1)先化简,再求值:(1-
1
x+1
1
x2-1
+(x-2)
,其中x=
6

(2)若x2-3x-1=0,求下列代数式的值.
x-
1
x
;②x2+
1
x2
答案

(1)(1-

1
x+1
1
x2-1
+(x-2)=
x
x+1
•(x+1)(x-1)+(x-2)=x(x-1)+(x-2)=x2-x+x-2=x2-2;

x=

6
代入上式得:

原式=(

6
)2-2=4;

(2)∵x2-3x-1=0,

∴x2-1=3x,

∴①x-

1
x
=
x2-1
x
=
3x
x
=3,

x2+

1
x2
=(x-
1
x
2+2=32+2=11.

单项选择题
选择题