actually i factored out the numerator a different way
i took out the 4 from the beginning and got 4(9x^2 - 6x + 1) then got (3x-1)(3x-1)
you neglected the fact that it -24x, not +24x when you factored it
for the denominator: (3x-1)(9x^2 - 1)
recognize the difference of squares in the denominator?
it will become(3x-1)(3x-1)(3x+1), so cancel and evaluate
just curious do you know about l'hopital's rule?
if you do, try to evaluate the limit using that rule and you see that the answer is different
just another example of when l'hopital's rule fails if you're interested in knowing that