题目内容
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 |
(3)
1 |
x+1 |
x-3 |
x2-1 |
x2-2x+1 |
(x-1)(x-3) |
(4)
3-x |
2x-4 |
5 |
x-2 |
(5)(1-
a-b |
a-2b |
a2-4b2 |
a2-4ab+4b2 |
分析:(1)把三个分式的分子分母同乘以它们的最简公分母x(x+1),再进行加减运算;
(2)先把x2-1因式分解,再将括号内的分式通分,最后约分即可;
(3)先将后面两个分式的分子分母因式分解再约分,最后和分式
通分可得问题答案;
(4)将括号内的分式通分,它们的最简公分母为x-2,把它们加减的结果和
约分即可;
(5)把括号内的分式通分,它们的最简公分母为a-2b,再把括号外面的分式分子分母因式分解,再把加减的结果和外面的分式约分,得问题答案.
(2)先把x2-1因式分解,再将括号内的分式通分,最后约分即可;
(3)先将后面两个分式的分子分母因式分解再约分,最后和分式
1 |
x+1 |
(4)将括号内的分式通分,它们的最简公分母为x-2,把它们加减的结果和
3-x |
2x-4 |
(5)把括号内的分式通分,它们的最简公分母为a-2b,再把括号外面的分式分子分母因式分解,再把加减的结果和外面的分式约分,得问题答案.
解答:解:(1)原式=
+
-
,
=
,
=
.
(2)原式=(x+1)(x-1)(
-
-
),
=x+1-x+1-(x+1)(x-1),
=-x2+3.
(3)原式=
-
×
,
=
-
,
=0.
(4)原式=
÷(
-
),
=
.
(5)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 |
点评:本题考查了分式的化简求值,在化简时注意分式的运算顺序和法则和因式分解的运用.
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