Question 63
For a real number $x$, where $x \notin\left\{0, \frac{1}{2}, \frac{2}{3}, 1,2\right\}$, simplify the expression
$$
\left(\frac{3 x^{-\frac{1}{3}}}{x^{\frac{2}{3}}-2 x^{-\frac{1}{3}}}-\frac{x^{\frac{1}{3}}}{x^{\frac{4}{3}}-x^{\frac{1}{3}}}\right)^{-1}-\left(\frac{1-2 x}{3 x-2}\right)^{-1}
$$
and compute its value for $x=\sqrt{3}$. Reduce the final result and, if necessary, rationalize the denominator.
$$
\left(\frac{3 x^{-\frac{1}{3}}}{x^{\frac{2}{3}}-2 x^{-\frac{1}{3}}}-\frac{x^{\frac{1}{3}}}{x^{\frac{4}{3}}-x^{\frac{1}{3}}}\right)^{-1}-\left(\frac{1-2 x}{3 x-2}\right)^{-1}
$$
and compute its value for $x=\sqrt{3}$. Reduce the final result and, if necessary, rationalize the denominator.