题目内容
计算：
(
+
+
+
)×(1+
+
+
)-(
+
+
)×(1+
+
+
+
)．
(
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分析：设
+
+
=a，然后把算式用a进行代换，再把算式展开进行化简消元即可求解．
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解答：解：设
+
+
=a，那么：
（
+
+
+
）×（1+
+
+
）-（
+
+
）×（1+
+
+
+
），
=（a+
）×（a+1）-a×（1+
+a），
=a2+a+
a+
-a-
a-a2，
=（a2-a2）+（a-a）+（
a-
a）+
，
=
．
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（
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=（a+
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=a2+a+
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=（a2-a2）+（a-a）+（
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=
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点评：此题考查了分数的巧算，关键是针对算式的特点，进行设未知数，从而达到抵消的目的．
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