Simplifying fractional indices: (p/q) = ([6p^3 - 2qp^2] / [q^4 - 3q^3p])

[HATLEY1997]

Can this be simplified any further?

 

[stapel]

Simplify using "flip" method:

[imath]\qquad \left(\dfrac{p}{q}\right)\, \div \, \left(\dfrac{6p^3 - 2qp^2}{q^4 - 3q^3 p}\right)[/imath]

My answer:

[imath]\qquad \dfrac{p(q^4 - 3q^3 p)}{q(6p^3 - 2qp^2)}[/imath]

Can this be simplified any further?

I'm not seeing that this has been simplified yet at all. To get started on that, try factoring the parentheticals. There is one cancellation.