Answer
$4q^2+2q+\frac{3}{2}+\frac{9}{2q-2}$
Work Step by Step
Re-arranging the order of the terms, the given is equivalent to
$$
(8q^3-4q^2-q+6)÷(2q-2)
.$$
Using the long division method shown below, then
$$\begin{aligned}
&
(8q^3-4q^2-q+6)÷(2q-2)
\\&=
4q^2+2q+\frac{3}{2}+\frac{9}{2q-2}
.\end{aligned}
$$
