Answer
$2x-3$
Work Step by Step
Factoring the expression and then cancelling common factors between the numerator and the denominator, then the given expression, $
\dfrac{8x^3-27}{4x^2+6x+9}
$, simplifies to
\begin{array}{l}\require{cancel}
\dfrac{(2x-3)(\cancel{4x^2+6x+9})}{\cancel{4x^2+6x+9}}
\\\\=
2x-3
.\end{array}
