# Thread: Need to find a domain, cannot factor.

1. ## Need to find a domain, cannot factor.

Hey guys. I have the following problem. I am supposed to find the domain of the following function:

$\displaystyle g(x) = \frac{1}{x^2 + 4} - \frac{1}{x^2 - 4}$

This means I'll need to factor the denominators to see what must be excluded from the domain:

$\displaystyle x^2 + 4$

and

$\displaystyle x^2 - 4$

I was able to factor $\displaystyle x^2 - 4$ easily enough and got:

$\displaystyle (x+2) (x-2)$

Which will exclude 2 and -2 from the domain. I'm lost on how to factor $\displaystyle x^2 + 4$.

Help!

2. Originally Posted by JennyFlowers
Hey guys. I have the following problem. I am supposed to find the domain of the following function:

$\displaystyle g(x) = \frac{1}{x^2 + 4} - \frac{1}{x^2 - 4}$

This means I'll need to factor the denominators to see what must be excluded from the domain:

$\displaystyle x^2 + 4$

and

$\displaystyle x^2 - 4$

I was able to factor $\displaystyle x^2 - 4$ easily enough and got:

$\displaystyle (x+2) (x-2)$

Which will exclude 2 and -2 from the domain. I'm lost on how to factor $\displaystyle x^2 + 4$.

Help!

$\displaystyle x^2+4$ does not factor over the real numbers.

you found the domain ... all reals except $\displaystyle x = \pm 2$.

you're done.

3. $\displaystyle x^2+ 4$ does not factor over the real numbers, therefore it is never equal to 0, since, if a polynomial is equal to 0 at x= a, it has (x- a) as a factor.