问题 解答题
1
a+1
-
a+3
a2-1
×
a2-2a+1
(a+1)(a-3)
,其中a2+2a-1=0.
答案

1
a+1
-
a+3
a2-1
×
a2-2a+1
(a+1)(a+3)

=

1
a+1
-
a+3
(a+1)(a-1)
×
(a-1)2
(a+1)(a+3)

=

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

当a2+2a-1=0即a2+2a=1时,原式=

2
1+1
=1.

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