One way of finding out the largest possible domain of that function, i.e. where the expression is defined is to use Wolfram Alpha within Mathematica:
= domain of (2x+9)/(x^2-5x-242x+9)
I added parenthesis to that expression, because I suspect that is what is meant.
If you click on the little plus symbol next to the solution, that comes up, you will get further information which might be useful.
I do believe that there is no function that does this directly in Mathematica 9, but I might be mistaken. Also, from hearsay I gather that there will be such a function in Mathematica 10.
