Question 37751
The key is to factor the numerator!  This is usually a tough factoring problem, but since the denominator has a factor of (x+6), you might just expect a factor of (x+6) in the numerator also.  Otherwise, there won't be anything to do in this problem.


I'd start with {{{2x^2+11x-6 }}}, and realize it has to start out 
{{{ (2x______)*(x_______) }}}.


Expecting the factor of x+6 to show up here, I would next try:
{{{ (2x______)*(x+6) }}}.


Since the LAST term has to be a -6, this means that the blank space left in the previous step will have to be -1.  Do you follow this?
{{{ (2x-1)*(x+6) }}}.  Now, check the middle term:  12x - 1x = + 11x.


{{{ (2x^2+11x-6)/(x+6)}}}
{{{((2x-1)(x+6))/(x+6) }}}


Divide out the x+6 factors, and you have a final answer of {{{2x-1}}}.


R^2 at SCC