Question 36434
I'm not sure I can read your problem to know what you meant, but I'll take a shot at it anyway.  I think you mean this:

{{{(x^2-x-12)/6)}}} divided by {{{ (x+3)/(x-4)}}}


Now factor everything, and invert the second fraction and multiply:
{{{((x-4)*(x+3))/6 }}} times {{{(x-4)/(x+3)}}}


The only factor that divides out is the factor of (x+3) in the first numerator and the second denominator, so the final answer is what is left over:
{{{((x-4)^2)/6}}}.


R^2 at SCC