题目内容
先阅读，再答题：由于
| 1 |
| 2×3 |
| 3-2 |
| 2×3 |
| 1 |
| 2 |
| 1 |
| 3 |
| 1 |
| 3×4 |
| 4-3 |
| 3×4 |
| 1 |
| 3 |
| 1 |
| 4 |
…
一般地有
| 1 |
| n×(n+1) |
| 1 |
| n |
| 1 |
| n+1 |
请根据上面的结论，计算：
| 1 |
| x |
| 1 |
| x(x+1) |
| 1 |
| (x+1)(x+2) |
| 1 |
| (x+2)(x+3) |
| 1 |
| (x+3)(x+4) |
分析：先根据给出的规律将原式展开，再进行分式的加法运算．
解答：解：原式=
+
-
+
-
+
-
+
-
，
=
-
=
．
| 1 |
| x |
| 1 |
| x |
| 1 |
| x+1 |
| 1 |
| x+1 |
| 1 |
| x+2 |
| 1 |
| x+2 |
| 1 |
| x+3 |
| 1 |
| x+3 |
| 1 |
| x+4 |
=
| 2 |
| x |
| 1 |
| x+4 |
=
| x+8 |
| x(x+4) |
点评：本题考查了分式的混合运算，解此题的关键是利用
=
-
将原式展开．
| 1 |
| n×(n+1) |
| 1 |
| n |
| 1 |
| n+1 |
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