Answer
$\pm 1;\pm {3}$
Work Step by Step
In a polinomial function like
$f\left( x\right) =a_{n}x^{n}+a_{n-1}x^{n-1}+\ldots a_{1}x+a_{0}$
If $p/q$, in lowest terms, is a rational zero of $f$, then p must be a factor of $a_0 $ and $q$ must be a factor of $a_n$.
Here
$f\left( x\right) =x^{5}-6x^{2}+9x-3\Rightarrow a_{n}=1;a_{0}=-3 $
Factors of $a_0$ are $\pm 1,\pm3$
Factors of $a_n$ are $\pm1 $
So the potential rational zeros are:
$\pm 1;\pm {3}$
