Answer
$${x{{\left( {2{x^2} + 1} \right)}^2}}$$
Work Step by Step
$$\eqalign{
& \frac{{3x - 1}}{{x{{\left( {2{x^2} + 1} \right)}^2}}} = \frac{A}{x} + \frac{{Bx + C}}{{2{x^2} + 1}} + \frac{{Dx + E}}{{{{\left( {2{x^2} + 1} \right)}^2}}} \cr
& {\text{We should multiply by }}x{\left( {2{x^2} + 1} \right)^2}{\text{ to clear the denominators}}{\text{.}} \cr} $$
