Answer
$\dfrac{f(x)}{g(x)}=7x^3+14x^2+25x+50+\dfrac{102}{x-2}$;
$x=2$ is not in the domain.
Work Step by Step
With the given functions, $f(x)=
7x^4-3x^2+2
,$ and $g(x)=
x-2
,$ using the long division below, then
\begin{array}{l}\require{cancel}
\dfrac{f(x)}{g(x)}
=\dfrac{
7x^4-3x^2+2
}{
x-2
}
\\\\\dfrac{f(x)}{g(x)}=
7x^3+14x^2+25x+50+\dfrac{102}{x-2}
.\end{array}
If $x=
2
,$ then the denominator, $
g(x)=x-2
,$ becomes zero. Since denominators cannot be zero, then $
x=2
$ is not in the domain of $\dfrac{f(x)}{g(x)}.$
