# AP,GP,HP

Algebra Level 4

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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