Answer
Vertical asymptotes$:\quad x=0$ and $x=3$
no holes
Work Step by Step
Locating Vertical Asymptotes, (page 395) tells us that for $f(x)=\displaystyle \frac{p(x)}{q(x)}$,
if p(x) and q(x) have NO common factors,
and a is a zero of the denominator $q(x)$ ,
then the line $x=a$ is a vertical asymptote.
BUT, if they DO have common factors,
after REDUCING the form of the function's equation,
the number a may not cause the denominator to be zero any more.
in which case there will be a hole at x=a.
The point is that both p(x) and q(x) have to be factored,
and if we can, then we reduce the expression for f(x).
------------------
$g(x)=\displaystyle \frac{x+3}{x(x-3)}$
$p(x)=x+3\qquad $... fully factored
$q(x)=x(x-3)\qquad $... fully factored
No common factors, no holes.
$q(x)=0$
$x(x-3)=0$
$x=0$ or $x=3$
Vertical asymptotes$:\quad x=0$ and $x=3$
