题目内容
![](http://thumb.1010pic.com/pic3/upload/images/201307/121/02b21eed.png)
x-1 |
3x2-6x |
5-4x |
x-2 |
②已知△ABC中,∠C=90°,按下列语句作图. (尺规作图,保留作图痕迹,不必写作法)
(1)作AB边的垂直平分线,交AC于点E,交AB于点F;
(2)连结CF.
(3)作∠BFC的平分线,交BC于G.
分析:①首先将括号里面通分,进而将分子分母因式分解化简得出即可;
②根据题意画出角平分线以及垂直平分线即可.
②根据题意画出角平分线以及垂直平分线即可.
解答:①解:∵x2+x-1=0,
∴x2+x=1,
÷(x-2-
),
=
÷[
-
]
=
÷
=
×
=
=
∴原式=
=
,
②如图所示
:
∴x2+x=1,
x-1 |
3x2-6x |
5-4x |
x-2 |
=
x-1 |
3x(x-2) |
(x-2)2 |
x-2 |
5-4x |
x-2 |
=
x-1 |
3x(x-2) |
x2-1 |
x-2 |
=
x-1 |
3x(x-2) |
x-2 |
(x+1)(x-1) |
=
1 |
3x(x+1) |
=
1 |
3(x2+x) |
∴原式=
1 |
3(x2+x) |
1 |
3 |
②如图所示
![](http://thumb.1010pic.com/pic3/upload/images/201309/89/69856459.png)
点评:此题主要考查了复杂作图以及分式的混合运算,正确将分式的分子与分母因式分解得出是解题关键.
![](http://thumb2018.1010pic.com/images/loading.gif)
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