若1/a+1/b=1/a+b则a/b+b/a=

若1/a+1/b=1/a+b则a/b+b/a=
若1/a+1/b=1/a+b则a/b+b/a=

若1/a+1/b=1/a+b则a/b+b/a=
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

1/a+1/b=1/a+b则
(a+b)*(1/a+1/b)=1
1+a/b+b/a+1=1
a/b+b/a=-1