Answer
$\{x\in R: x \neq 3\} =(-\infty , 3) \cup (3, \infty).$
Work Step by Step
The domain of $f(x)=\frac{1}{x-3}$ is the set of all real numbers $x$ for which $\frac{1}{3-x}$ is defined as a real number. We know a rational expression is not defined where the denominator is zero, so we must find all values of $x$ for which $$3-x =0.$$ We add $x$ to both sides to get $$3=x.$$ Thus we know $\frac{1}{3-x}$ is not defined when $x=3$. This means the domain of $f(x)=\frac{1}{3-x}$ is the set af all real numbers $x$ for which $x\neq 3$
In set notation, the domain is $\{x\in R: x \neq 3\}.$
In interval notation, the domain is $(-\infty , 3) \cup (3, \infty).$