You are correct! The problems that can arise with a function domain are:
- Denominators that become zero
- Even-degree roots with negative input
- Logarithms with negative or zero input
In this case, you have a denominator, and you don't have roots nor logarithms. This means that your only concern must be the denominator, specifically, it cannot be zero.
And you simply have
So, the domain of this function includes every number except 3.