Multiply top and bottom by the conjugate, \(\displaystyle \sqrt{x+9}+3\)
Then it reduces down to something you can deal with.
By the way, I assume you mean \(\displaystyle \frac{\sqrt{x+9}-3}{x}\).
You have \(\displaystyle \sqrt{x+9}-\frac{3}{x}\) written.
That is why grouping symbols are important.
