# Domain

#### Lucyzzz

8x/x2 + 9, I tried moving the 9 given me x2=-9 so x= square room of -9 that is impossible, I am pretty confused.

#### Plato

MHF Helper
8x/x2 + 9, I tried moving the 9 given me x2=-9 so x= square room of -9 that is impossible, I am pretty confused.
Well until you learn to post your questions in a correct format you will remain confused!
Here is exactly what you posted: $$\displaystyle \frac{8x}{x^2}+9$$ is that what you meant? I think not.
I think that you meant: $$\displaystyle \frac{8x}{x^2+9}$$ which has domain, all real numbers.

#### Lucyzzz

Yes sorry for the confusion. I am not good with technology thanks for your help.

#### Debsta

MHF Helper
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!)

#### Lucyzzz

thanks so much, Debsta.