问题 解答题
先化简,再求值:
(1)(1-
1
a-1
a2-4a+4
a2-a
,其中a=-1;
(2)(
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=

a-2
a-1
×
a(a-1)
(a-2)2

=

a
a-2

当a=1时,原式=

1
1-2
=-1;

(2)原式=

(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

∵x满足x2-x-1=0,

∴x2=x+1,

∴原式=

x+1
x+1
=1.

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