题目内容
计算：| 1 |
| (x+1)(x+2) |
| 1 |
| (x+2)(x+3) |
| 1 |
| (x+3)(x+4) |
| 1 |
| (x+100)(x+101) |
分析：因分式复杂，观察式中分母的特点，恰当运用通分的相关策略与技巧．本题采用拆项抵消法．
解答：解：
+
+
+…+
=
-
+
-
+…+
-
=
-
=
．
| 1 |
| (x+1)(x+2) |
| 1 |
| (x+2)(x+3) |
| 1 |
| (x+3)(x+4) |
| 1 |
| (x+100)(x+101) |
=
| 1 |
| x+1 |
| 1 |
| x+2 |
| 1 |
| x+2 |
| 1 |
| x+3 |
| 1 |
| x+100 |
| 1 |
| x+101 |
=
| 1 |
| x+1 |
| 1 |
| x+101 |
=
| 100 |
| (x+1)(x+101) |
点评：本题考查了分式的加减运算，难度较大．解题的关键是熟知
=
-
．
| 1 |
| (x+1)(x+2) |
| 1 |
| x+1 |
| 1 |
| x+2 |
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