Question 106091
You're here.
{{{(x^2-9)/(x-3)}}}
You're not way off. But you are a little off. 
You can simplify {{{x^2-9}}} by factoring. 
Hint : Use the denominator as one factor.
{{{(x^2-9)=(x-3)*(x+a)}}}
If you expand the right hand side using the FOIL method, you can compare terms, find "a" and move forward. 
If you get stuck, post another question.