题目内容
先化简,后求值:(1+
)÷
,其中x=3.
1 |
x-2 |
x2-2x+1 |
x2-4 |
考点:分式的化简求值
专题:
分析:首先将括号里面通分,能分解因式的分解因式,进而化简后求值得出.
解答:解:(1+
)÷
,
=(
+
)×
=
×
=
,
当x=3时,原式=
=
.
1 |
x-2 |
x2-2x+1 |
x2-4 |
=(
x-2 |
x-2 |
1 |
x-2 |
(x+2)(x-2) |
(x-1)2 |
=
x-1 |
x-2 |
(x+2)(x-2) |
(x-1)2 |
=
x+2 |
x-1 |
当x=3时,原式=
3+2 |
3-1 |
5 |
2 |
点评:此题主要考查了分式的化简求值问题,正确将分式分解因式是解题关键.
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