Question 36479
I see two factoring errors.  First the  {{{3x^2 -x-4}}} factors into {{{3x-4)*(x+1) }}}.  Second, where you have a factor of (2x-2), I think it should be (x-2).


In your last step you have this:
(x + 4)(3x^2 - x - 4)
(3x + 4)(3x - 4)(2x - 2) 


I think it should be this:
(x + 4)(3x-4)(x+1)
(3x + 4)(3x - 4)(x - 2) 


Then the final answer should be
{{{((x+4)*(x+1))/((3x+4)*(x-2)) }}}


R^2 at SCC