\(\frac{-x^2\left(x-2\right)+x-2}{x\left(4x-9\right)}\ge0\)
\(\Leftrightarrow\frac{\left(1-x\right)\left(1+x\right)\left(x-2\right)}{x\left(4x-9\right)}\ge0\)
\(\Rightarrow\left[{}\begin{matrix}x\le-1\\0< x\le1\\\frac{9}{4}< x\le2\end{matrix}\right.\)