题目内容

直接写出化简结果:
(1)
4xy
16x2y
=
1
4x
1
4x

(2)
a(a+b)
b(a+b)
=
a
b
a
b

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

(4)
ax+ay
x2-y2
=
a
x-y
a
x-y

(5)
x2-16
x2+8x+16
=
x-4
x+4
x-4
x+4

(6)
x2-9
2x+6
=
x-3
2
x-3
2
分析:(1)(2)直接约分,(3)将分母中的x、y交换位置后再约分,(4)(5)(6)先因式分解再约分.
解答:解:(1)原式=
1
4x

(2)原式=
a
b

(3)原式=
x-y
(x-y)2
=
1
x-y

(4)原式=
a(x+y)
(x-y)(x+y)
=
a
x-y

(5)原式=
(x-4)(x+4)
(x+4)2
=
x-4
x+4

(6)原式=
(x-3)(x+3)
2(x+3)
=
x-3
2

故答案为
1
4x
a
b
1
x-y
a
x-y
x-4
x+4
x-3
2
点评:本题考查了约分,找到分子、分母中的公因式是解题的关键.
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