If abc = 1 then show that: 1/(1+a+b^-1) + 1/(1+b+c^-1) + 1/(1+c+a^-1) =1

Since  abc=1
Therefore  c=1/ab

1/(1+a+b^-1) + 1/(1+b+c^-1) + 1/(1+c+a^-1)

=1/(1+a+1/b)+1/(1+b+1/c)+1/(1+c+1/a)

On putting  c=1/ab

=1/(1+a+1/b)+1/(1+b+ab)+1/(1+1/ab+1/a)

=b/(1+b+ab)+1/(1+b+ab)+ab/(1+b+ab)

=(1+b+ab) /(1+b+ab)

=1
Hence proved

Deepak Rajoria
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