题目内容
化简求值：
÷
+
，其中x=2．
| x2-2x+1 |
| x2-1 |
| x2-x |
| x+1 |
| 1 |
| x-1 |
分析：先将分子、分母分别因式分解，然后约分即可．
解答：解：原式=
•
+
=
+
=
+
=
=
，
将x=2代入上式得，原式=
=
．
| (x-1)2 |
| (x-1)(x+1) |
| x+1 |
| x(x-1) |
| 1 |
| x-1 |
=
| 1 |
| x |
| 1 |
| x-1 |
=
| x-1 |
| x(x-1) |
| x |
| x(x-1) |
=
| 2x-1 |
| x(x-1) |
=
| 2x-1 |
| x2-x |
将x=2代入上式得，原式=
| 2×2-1 |
| 22-2 |
| 3 |
| 2 |
点评：本题考查了分式的化简求值，懂得因式分解及分式的加减乘除法则是解题的关键．
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