Answer
$\left(\dfrac{f}{g}\right)(3)=-\dfrac{23}{4}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To find the expression, $
\left(\dfrac{f}{g}\right)(3)
,$ given that
\begin{array}{l}\require{cancel}
f(x)=3x^2-4 \text{ and }
\\g(x)=x^2-3x-4
,\end{array}
use the definition of the appropriate function operation. Then substitute $x$ with $3.$
$\bf{\text{Solution Details:}}$
Using $\left(\dfrac{f}{g}\right)(x)=\dfrac{f(x)}{g(x)},$ then
\begin{array}{l}\require{cancel}
\left(\dfrac{f}{g}\right)(x)=\dfrac{3x^2-4}{x^2-3x-4}
.\end{array}
Sustituting $x$ with $3,$ then
\begin{array}{l}\require{cancel}
\left(\dfrac{f}{g}\right)(3)=\dfrac{3(3)^2-4}{(3)^2-3(3)-4}
\\\\
\left(\dfrac{f}{g}\right)(3)=\dfrac{3(9)-4}{(9)-3(3)-4}
\\\\
\left(\dfrac{f}{g}\right)(3)=\dfrac{27-4}{9-9-4}
\\\\
\left(\dfrac{f}{g}\right)(3)=\dfrac{23}{-4}
\\\\
\left(\dfrac{f}{g}\right)(3)=-\dfrac{23}{4}
.\end{array}