A rational expression, like the one you have, is undefined when the denominator is 0.

I think you may have then tried to solve \(\displaystyle x^2 +9 =0\) getting \(\displaystyle x^2=-9\). As you said, this is impossible. So far, so good.

Now, the **domain **of a function is the set of all numbers that x can be. Now, is there any value of x that makes this rational expression undefined? No there isn't because, as you said, there is no x-value that when squared gives -9.

So therefore x can be anything, so the **domain** is the set of all real numbers (there's nothing that x can't be!)