Answer
$\displaystyle \frac{1}{3}$
Work Step by Step
see: Rules for Limits
Let $a, A$, and $B$ be real numbers,
and let $f$ and $g$ be functions such that
$\displaystyle \lim_{x\rightarrow a}f(x)=A$ and $\displaystyle \lim_{x\rightarrow a}g(x)=B$.
4. $\displaystyle \lim_{x\rightarrow a}\frac{f(x)}{g(x)}=\frac{\lim_{x\rightarrow a}f(x)}{\lim_{x\rightarrow a}g(x)}=\frac{A}{B}$ if $B\neq 0$
(The limit of a quotient is the quotient of the limits, provided the limit of the
denominator is not zero.)
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$\displaystyle \lim_{x\rightarrow 4}\frac{f(x)}{g(x)}=\frac{\lim_{x\rightarrow 4}f(x)}{\lim_{x\rightarrow 4}g(x)}$
$=\displaystyle \frac{9}{27}=\frac{1}{3}$
