Answer
$\dfrac{2x-1}{2}$
Work Step by Step
Factoring the expressions and cancelling the common factors between the numerator and the denominator, the given expression, $
(2x^2+3x-2)\div(2x+4)
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{2x^2+3x-2}{2x+4}
\\\\=
\dfrac{(2x-1)(x+2)}{2(x+2)}
\\\\=
\dfrac{(2x-1)(\cancel{x+2})}{2(\cancel{x+2})}
\\\\=
\dfrac{2x-1}{2}
.\end{array}
