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Result is directly proportional to A

Result is inversely proportional to B

So, I assume two constants, alpha and beta such that:

Result = (A^alpha)/(B^beta)

Now, if I know I want to solve for alpha and beta but is this the right approach to take to get the value of Result for any given A and B?

(Actually, I could have assumed Result = k. (A/B) but I am not sure that my result follows such a simple proportionality which is why I assumed alpha and beta). Any input on this is appreciated. Thanks