Answer
$8-\dfrac{9}{x}+\dfrac{3}{2x^2}$
Work Step by Step
Dividing the denominator to each of the terms of the numerator, the given expression, $
\dfrac{64x^3-72x^2+12x}{8x^3}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{64x^3}{8x^3}-\dfrac{72x^2}{8x^3}+\dfrac{12x}{8x^3}
\\\\=
8-\dfrac{9}{x}+\dfrac{3}{2x^2}
.\end{array}