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