若1/a+1/b=1/a+b则a/b+b/a=

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答案和解析

已知
1/a+1/b=1/(a+b)
即
(a+b)/ab=1/(a+b)
(a+b)²=ab
则
a/b+b/a
=(a²+b²)/ab
=(a²+2ab-2ab+b²)/ab
=(a²+2ab+b²)/ab-2
=(a+b)²/ab-2
=1-2
=-1

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