Answer
$\dfrac{3x^2-7x-4}{(3x-4)(9x^2+12x+16)}$
Work Step by Step
Factoring the given expression, $
\dfrac{x}{9x^2+12x+16}-\dfrac{3x+4}{27x^3-64}
,$ results to
\begin{array}{l}\require{cancel}
\dfrac{x}{9x^2+12x+16}-\dfrac{3x+4}{(3x-4)(9x^2+12x+16)}
.\end{array}
Using the $LCD=
(3x-4)(9x^2+12x+16)
$, the expression above simplifies to
\begin{array}{l}\require{cancel}
\dfrac{(3x-4)(x)-1(3x+4)}{(3x-4)(9x^2+12x+16)}
\\\\=
\dfrac{3x^2-4x-3x-4}{(3x-4)(9x^2+12x+16)}
\\\\=
\dfrac{3x^2-7x-4}{(3x-4)(9x^2+12x+16)}
.\end{array}
