#### Answer

$z' = \frac{9x^{2}-24x-4}{(3x^{2}+x)^{2}}$

#### Work Step by Step

$z = \frac{4-3x}{3x^{2}+x}$
$z' = \frac{(3x^{2}+x)(-3) - (4-3x)(6x+1)}{(3x^{2}+x)^{2}}$
$z'= \frac{-9x^{2}-3x-24x-4+18x^{2}+3x}{(3x^{2}+x)^{2}}$
$z' = \frac{9x^{2}-24x-4}{(3x^{2}+x)^{2}}$