Intermediate Algebra (6th Edition)

$2x-3$
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}