Answer
$t-1+\frac{{2t}}{{2t^3+1}}$
Work Step by Step
Re-arranging the order of the terms, the given is equivalent to
$$
(2t^4-2t^3+3t-1)÷(2t^3+1)
.$$
Using the long division method shown below, then
$$\begin{aligned}
&
(2t^4-2t^3+3t-1)÷(2t^3+1)
\\&=
t-1+\frac{\color{red}{2t}}{\color{blue}{2t^3+1}}
.\end{aligned}
$$
