问题 解答题
(1)计算:
a
a-1
-
a-1
a-2

(2)若a-1<0,比较
a
a-1
a-1
a-2
的大小.
答案

(1)原式=

a(a-2)
(a-1)(a-2)
-
(a-1)2
(a-1)(a-2)

=

a(a-2)-(a-1)2
(a-1)(a-2)

=

a2-2a-a2+2a-1
(a-1)(a-2)

=-

1
(a-1)(a-2)

(2)根据(1)得:

a
a-1
-
a-1
a-2
=-
1
(a-1)(a-2)

当a-1<0时,a-2<0,则(a-1)(a-2)>0,

∴-

1
(a-1)(a-2)
<0,

a
a-1
a-1
a-2

判断题
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