Answer
$x=-\dfrac{7}{24}$
Work Step by Step
Multiply $3x$ to both sides to obtain:
\begin{array}{ccc}
\\&3x(\frac{2}{x} - \frac{4}{3x})&=&3x(8+\frac{3}{x})
\\&3x(\frac{2}{x}) - 3x(\frac{4}{3x})&=&3x(8)+3x(\frac{3}{x})
\\&\frac{6x}{x} - \frac{12x}{3x}&=&24x+\frac{9x}{x}
\\&6-4&=&24x+9
\\&2&=&24x+9
\\&2-9&=&24x
\\&-7&=&24x
\end{array}
Divide $24$ to both sides of the equation to obtain:
\begin{array}{ccc}
&\dfrac{-7}{24} &= &\dfrac{24x}{24}
\\&-\dfrac{7}{24}&=&x
\end{array}
