问题 解答题
计算下列各题.
(1)
3
x
-
6
1-x
-
x+5
x2-x

(2)(x2-1)(
1
x-1
-
1
x+1
-1)

(3)
1
x+1
-
x-3
x2-1
-
x2-2x+1
(x-1)(x-3)

(4)
3-x
2x-4
÷(x+2-
5
x-2
)

(5)(1-
a-b
a-2b
a2-4b2
a2-4ab+4b2
答案

(1)原式=

3(x-1)
x(x-1)
+
6x
x(x-1)
-
x+5
x(x-1)

=

8(x-1)
x(x-1)

=

8
x

(2)原式=(x+1)(x-1)(

x+1
(x+1)(x-1)
-
x-1
(x+1)(x-1)
-
(x+1)(x-1)
(x+1)(x-1)
),

=x+1-x+1-(x+1)(x-1),

=-x2+3.

(3)原式=

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

=

1
x+1
-
1
x-1

=0.

(4)原式=

3-x
2(x-2)
÷(
(x+2)(x-2)
x-2
-
5
x-2
),

=

1
2(x+3)

(5)原式=(

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

=

-b
a-2b
×
(a-2b) 2
(a+2b)(a-2b)

=-

b
a+2b

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