先化简再求值:(1)(1+1x-2)÷x2-12x-4,其中,x=3.(2)(1a-b-1a+b)÷ba2-2ab+b2,其中a=1+2,b=1-2.-数学

题目简介

先化简再求值:(1)(1+1x-2)÷x2-12x-4,其中,x=3.(2)(1a-b-1a+b)÷ba2-2ab+b2,其中a=1+2,b=1-2.-数学

题目详情

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
题型:解答题难度:中档来源:不详

答案

(1)(1+class="stub"1
x-2
)÷
x2-1
2x-4

=class="stub"x-2+1
x-2
÷
(x+1)(x-1)
2(x-2)

=class="stub"x-1
x-2
2(x-2)
(x+1)(x-1)

=class="stub"2
x+1

当x=3时,原式=class="stub"2
3+1
=class="stub"1
2


(2)(class="stub"1
a-b
-class="stub"1
a+b
)÷class="stub"b
a2-2ab+b2

=
a+b-(a-b)
(a+b)(a-b)
÷class="stub"b
(a-b)2

=class="stub"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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