Question

If abc =1,show that (1+a+1/b)^-1 +(1+b+1/c)^-1+(1+c+1/a)^-1=1​

Answer 1

Step-by-step explanation:

abc=1

⟹c=1/ab

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

=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