题目内容
计算
+
(1+
)+
(1+
)(1+
)+
(1+
)(1+
)(1+
)-(1+
)(1+
)(1+
)(1+
)．
| 1 |
| a |
| 1 |
| b |
| 1 |
| a |
| 1 |
| c |
| 1 |
| a |
| 1 |
| b |
| 1 |
| d |
| 1 |
| a |
| 1 |
| b |
| 1 |
| c |
| 1 |
| a |
| 1 |
| b |
| 1 |
| c |
| 1 |
| d |
分析：原式后两项提取公因式，化简后后两项再提取公因式，依此类推即可得到结果．
解答：解：原式=
+
（1+
）+
（1+
）（1+
）+（1+
）（1+
）（1+
）（
-1-
）
=
+
（1+
）+（1+
）（1+
）（
-1+
）
=
+（1+
）（
-1-
）
=
-1-
=-1．
| 1 |
| a |
| 1 |
| b |
| 1 |
| a |
| 1 |
| c |
| 1 |
| a |
| 1 |
| b |
| 1 |
| a |
| 1 |
| b |
| 1 |
| c |
| 1 |
| d |
| 1 |
| d |
=
| 1 |
| a |
| 1 |
| b |
| 1 |
| a |
| 1 |
| a |
| 1 |
| b |
| 1 |
| c |
| 1 |
| c |
=
| 1 |
| a |
| 1 |
| a |
| 1 |
| b |
| 1 |
| b |
=
| 1 |
| a |
| 1 |
| a |
=-1．
点评：此题考查了分式的混合运算，分式的加减运算关键是通分，通分的关键是找最简公分母；分式的乘除运算关键是约分，约分的关键是找公因式．
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