Complex function completely simplified and i cant figure out how?

Question

I've been working through some homework on derivatives, particularly complex derivatives, with the following question:

calculate the derivative of function f defined on ]-∞ ; -1]U[1;+∞[ by:

f(x) = $(2x² +1) √x²-1/frac 3x³$

in the correction it has been simplified down to :

12x⁴(x²-1)+(2x²+1)3x⁴-9x²(2x²+1)(x²-1) / 9x⁶ √x²-1

and then to :

1 / x⁴ √x²-1

i cant figure out how they've manage to simplify down more than 3 terms to one number on the numerator.. The only thing i've really understood is that 3x³ seems to have been a factor at some point in the simplification beforehand. thanks in advance