试题

题目:
把下列各分式约分化简
(1)
3x3y4
18x5y5
(2)
-6xy
3y2
(3)
9x
-18x3
(4)
-3pq
-9pq
(5)
2(x-y)2
8(x-y)3
(6)
4a(x-1)
12ab(1-x)
(7)
m
m3-m2
(8)
12x2y(x-y)2
15x3y5(x2-y2)
(9)
b-a
a2-b2
(10)
9x2-18x+9
3x-3
(11)
a2-5a+6
a2-a-2
(12)
a2-b2-c2+2bc
a2+b2-c2+2ab

答案
解:(1)
3x3y4
18x5y5
=
1
6x2y


(2)
-6xy
3y2
=-
2
y


(3)
9x
-18x3
=-
1
2x2


(4)
-3pq
-9pq
=
1
3


(5)
2(x-y)2
8(x-y)3
=
1
4(x-y)


(6)
4a(x-1)
12ab(1-x)
=-
1
3b


(7)
m
m3-m2

=
m
m2(m-1)

=
1
m2-m


(8)
12x2y(x-y)2
15x3y5(x2-y2)

=
12x2y(x-y)2
15x3y5(x-y)(x+y)

=
4(x-y) 
5x y4(x+y)

(9)
b-a
a2-b2
=-
1
a+b


(10)
9x2-18x+9
3x-3

=
9(x-1)2
3(x-1)

=3x-3;

(11)
a2-5a+6
a2-a-2

=
(a-2)(a-3)
(a-2)(a+1)

=
a-3
a+1


(12)
a2-b2-c2+2bc
a2+b2-c2+2ab

=
a2-(b+c)2
(a+b)2-c2

=
(a-b-c)(a+b+c)
(a+b-c)(a+b+c)

=
a-b-c
a+b-c

解:(1)
3x3y4
18x5y5
=
1
6x2y


(2)
-6xy
3y2
=-
2
y


(3)
9x
-18x3
=-
1
2x2


(4)
-3pq
-9pq
=
1
3


(5)
2(x-y)2
8(x-y)3
=
1
4(x-y)


(6)
4a(x-1)
12ab(1-x)
=-
1
3b


(7)
m
m3-m2

=
m
m2(m-1)

=
1
m2-m


(8)
12x2y(x-y)2
15x3y5(x2-y2)

=
12x2y(x-y)2
15x3y5(x-y)(x+y)

=
4(x-y) 
5x y4(x+y)

(9)
b-a
a2-b2
=-
1
a+b


(10)
9x2-18x+9
3x-3

=
9(x-1)2
3(x-1)

=3x-3;

(11)
a2-5a+6
a2-a-2

=
(a-2)(a-3)
(a-2)(a+1)

=
a-3
a+1


(12)
a2-b2-c2+2bc
a2+b2-c2+2ab

=
a2-(b+c)2
(a+b)2-c2

=
(a-b-c)(a+b+c)
(a+b-c)(a+b+c)

=
a-b-c
a+b-c
考点梳理
约分.
对于分子分母为单项式的分式,直接约分;对于分子分母是多项式的分式,先因式分解,再约分.
本题考查了约分,熟悉因式分解是解题的关键.
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