How do you find the domain of f(x)=x/(3x-1)?

$\frac{x}{3 x - 1}$ is well defined for all $x \in \mathbb{R}$ except when $3 x - 1 = 0$.
$3 x - 1 = 0$ when $x = \frac{1}{3}$.
So the domain of $f \left(x\right)$ is $\left\{x \in \mathbb{R} : x \ne \frac{1}{3}\right\}$