问题 解答题
已知a=2+
2
,求(
3a
a+1
-
a
a-1
)÷
a
a2-1
的值.
答案

原式=[

3a(a-1)
(a+1)(a-1)
-
a(a+1)
(a+1)(a-1)
]•
(a+1)(a-1)
a

=

3a2-3a-a2-a
(a+1)(a-1)
(a+1)(a-1)
a

=

2a2-4a
(a+1)(a-1)
(a+1)(a-1)
a

=

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

=2a-4,(4分)

当a=2+

2
时,原式=2(2+
2
)-4=2
2
.(7分)

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