问题 解答题
先化简再求值:
(1)(1+
1
x-2
x2-1
2x-4
,其中,x=3.
(2)(
1
a-b
-
1
a+b
)
÷
b
a2-2ab+b2
,其中a=1+
2
b=1-
2
答案

(1)(1+

1
x-2
)÷
x2-1
2x-4

=

x-2+1
x-2
÷
(x+1)(x-1)
2(x-2)

=

x-1
x-2
2(x-2)
(x+1)(x-1)

=

2
x+1

当x=3时,原式=

2
3+1
=
1
2

(2)(

1
a-b
-
1
a+b
)÷
b
a2-2ab+b2

=

a+b-(a-b)
(a+b)(a-b)
÷
b
(a-b)2

=

2b
(a+b)(a-b)
(a-b)2
b

=

2(a-b)
a+b

当a=1+

2
,b=1-
2
时,原式=
2(1+
2
-1+
2
)
1+
2
+1-
2
=2
2

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