题目内容
用简便方法计算：
（1+
+
+
）×（
+
+
+
）-（1+
+
+
+
）×（
+
+
）=
．
（1+
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分析：本题可利用换元法进行解决，设A=1+
+
+
，B=
+
+
，所以原式化为a×（b+
）-（a+
）×b=
（a-b）=
，即：（1+
+
+
）×（
+
+
+
）-（1+
+
+
+
）×（
+
+
）=
．
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解答：解：：（1+
+
+
）×（
+
+
+
）-（1+
+
+
+
）×（
+
+
）
设设a=1+
+
+
，b=
+
+
，所以原式化为：
a×（b+
）-（a+
）×b
=a×b+
×a-a×b-
×b，
=
×（a-b），
=
×[（1+
+
+
）-（
+
+
）]，
=
．
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设设a=1+
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a×（b+
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=a×b+
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=
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=
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=
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点评：换元法也是分数巧算中常用的方法．
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