Given that \(\alpha,\beta,a,b\) are in \(AP\) ;\(\alpha,\beta,c,d\) are in \(GP\) and \(\alpha,\beta,e,f\) are in \(HP\).

If \(b,d,f\) are in \(GP\) then find \(\large{\frac{\alpha ^6-\beta ^6}{\alpha \beta (\alpha ^4-\beta^4)}}\)

Clarification \(\alpha\) is not equal to \(\beta\)

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