问题 解答题
计算:
(1)(
3x
x-2
-
x
x+2
)÷(
x
x2-4

(2)(
a2
b
2(-
b2
a
3÷(-
b
a
4
(3)先化简再求值:
x-1
x2-4x+4
x2-4
x2-1
,其中x=3.
(4)已知:
a
a-b
=2,求
(a2+ab)(a-5b)
(a-b)(a2-5ab)
的值
答案

(1)原式=

x2+6x- x2+2x
(x-2)(x+2)
÷
x
(x+2)(x-2)

=

2x(x+8)
(x+2)(x-2)
(x+2)(x-2)
x

=2x+8

(2)原式=

a4
b2
(-
b6
a3
)
b4
a4

=-a5

(3)原式=

x-1
(x-2)2
 • 
(x+2)(x-2)
(x+1)(x-1)

=

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

=

5
4

(4)原式=

a•(a+b)•(a-5b)
(a-b)•a•(a-5b)

=

a+b
a-b

a
a-b
=2,即a=2a-2b,即a=2b

所以原式=

3b
b
=3.

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单项选择题