Answer
The answer is $t-1+\frac{2t}{2t^3+1}$
Work Step by Step
$(2t^4-2t^3+3t-1) \div (2t^3+1)$
$t-1$
_________________________
$2t^3+1) 2t^4-2t^3+3t-1$
$-2t^3-t$
_________________________
$-2t^3+2t-1$
$2t^3+1$
_________________________
$2t$
The answer is $t-1+\frac{2t}{2t^3+1}$.
