#### Answer

The domain is all real numbers, except $4$ and $-4$.

#### Work Step by Step

To find the values of $x$ that create a zero in the denominator, set the denominator equal to zero and solve.
$3x^{2}-48=0$
Factor
$3(x^{2}-16)=0$
Using the Zero Product Property
$3=0$ and $x^{2}-16=0$
The first equation is false.
The second equation
$x^{2}-16=0$
Add $16$ to both sides
$x^{2}=16$
Square root both sides
$x=4$ and $x=-4$
Therefore, the two values that $x$ cannot be are $4$ and $-4$. The domain is all real numbers EXCEPT these two values.