Question 10335
If your question is this, as I suspect it is:
{{{3/(x + 2) + x/(x^2-4) }}} 


then you missed it.  If it's NOT what I am suggesting, then you still missed it!!  Sorry about that!


You are correct to factor the second denominator.  
{{{3/(x + 2) + x/((x-2)(x+2) )}}} 


Next, since this is an addition problem, you must find a common denominator, which is (x-2)(x+2).  The second fraction already has the common denominator, so it is good to go!!  However, the first fraction is missing something.  It's missing a factor of (x-2).  So you have to multiply numerator and denominator of the first fraction by (x+2).  It looks like this:

{{{(3/(x + 2))*((x-2)/(x-2)) + x/((x-2)(x+2) )}}}


Now, put down the common denominator for the denominator of your answer, and for the numerator of your answer, you have to add the numerators of the two fractions:

{{{(3x-6 + x)/((x-2)(x+2) )}}}


Combine like terms in the numerator:
{{{(4x-6 )/((x-2)(x+2) )}}}


You might try to factor the numerator, but it doesn't reduce, so either the previous answer or the factored form is acceptable:
{{{(2(2x-3))/((x-2)(x+2) )}}}


R^2 at SCC