Answer
$t+5+\frac{21}{2t-6}$
Work Step by Step
Re-arranging the order of the terms, the given is equivalent to
$$
(2t^2+4t-9)÷(2t-6)
.$$
Using the long division method shown below, then
$$\begin{aligned}
&
(2t^2+4t-9)÷(2t-6)
\\&=
t+5+\frac{21}{2t-6}
.\end{aligned}
$$
