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(1+
1
3
+
1
5
+
1
7
)×(
1
3
+
1
5
+
1
7
+
1
9
)-(1+
1
3
+
1
5
+
1
7
+
1
9
)×(
1
3
+
1
5
+
1
7
)
分析:因每个项中都有
1
3
+
1
5
+
1
7
,可设
1
3
+
1
5
+
1
7
=a,然后再进行计算.据此解答.
解答:解:设
1
3
+
1
5
+
1
7
=a,
(1+
1
3
+
1
5
+
1
7
)×(
1
3
+
1
5
+
1
7
+
1
9
)-(1+
1
3
+
1
5
+
1
7
+
1
9
)×(
1
3
+
1
5
+
1
7
)

=(1+a)×(a+
1
9
)-(1+a+
1
9
)×a
=a+
1
9
+a2+
1
9
a-a-a2-
1
9
a
=
1
9
点评:本题的难点是根据每个项中都有
1
3
+
1
5
+
1
7
,可设
1
3
+
1
5
+
1
7
=a,然后再进行计算.
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