SOLUTION: abc=1 show that 1/(1+a+1/b)+1/(1+b+1/c)+1/(1+c+1/a)=1

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Question 940411: abc=1
show that
1/(1+a+1/b)+1/(1+b+1/c)+1/(1+c+1/a)=1
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
abc=1
show that
1%2F%281%2Ba%2B1%2Fb%29%2B1%2F%281%2Bb%2B1%2Fc%29%2B1%2F%281%2Bc%2B1%2Fa%29=1
since abc=1,  a=1%2F%28bc%29 and 1%2Fa=bc.  Substituting



1%2F%281%2B1%2F%28bc%29%2B1%2Fb%29%2B1%2F%281%2Bb%2B1%2Fc%29%2B1%2F%281%2Bc%2Bbc%29

Multiply 1st fraction by %28bc%29%2F%28bc%29 and 2nd fraction by c%2Fc

bc%2F%28bc%2B1%2Bc%29%2Bc%2F%28c%2Bbc%2B1%29%2B1%2F%281%2Bc%2Bbc%29

All the denominators are the same

%28bc%2Bc%2B1%29%2F%28bc%2B1%2Bc%29

which is just 1

Edwin