1. The problem statement, all variables and given/known data If a+b+c=0 then ( (b-c)/a + (c-a)/b + (a-b)/c )( a/(b-c) + b/(c-a) + c/(a-b) ) is equal to: Ans: 9 2. Relevant equations AM>=GM>=HM Equality holds when all numbers are equal. 3. The attempt at a solution I tried using AM>=GM. ( (b-c)/a + (c-a)/b + (a-b)/c + a/(b-c) + b/(c-a) + c/(a-b) )/6 >= 1 The AM side doesn't seem to simplify. All the numbers on the GM side cancel leaving me with one. I know I need to convert it into some form of a+b+c=0 but can't figure out how.