Answer
$2x^2-x-2+\dfrac{2}{2x+1}$
Work Step by Step
Using the long division method below, then
\begin{array}{l}\require{cancel}
(
4x^3-5x
)\div(
2x+1
)
\\=
2x^2-x-2+\dfrac{2}{2x+1}
.\end{array}
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