ĐKXĐ: \(x\notin\left\{0;\dfrac{3}{2};-\dfrac{3}{2};2\right\}\)
\(\left(\dfrac{5x}{2x^2-3x}+\dfrac{2}{2x^2-3x}-\dfrac{2x-33}{9-4x^2}\right):\dfrac{4x-8}{6x+9}\)
\(=\left(\dfrac{5x-2}{x\left(2x-3\right)}+\dfrac{2x-33}{\left(2x-3\right)\left(2x+3\right)}\right)\cdot\dfrac{3\left(2x+3\right)}{4\left(x-2\right)}\)
\(=\dfrac{\left(5x-2\right)\left(2x+3\right)+x\left(2x-33\right)}{x\left(2x-3\right)\left(2x+3\right)}\cdot\dfrac{3\left(2x+3\right)}{4\left(x-2\right)}\)
\(=\dfrac{10x^2+15x-4x-6+2x^2-33x}{x\left(2x-3\right)}\cdot\dfrac{3}{4\left(x-2\right)}\)
\(=\dfrac{12x^2-22x-6}{x\left(2x-3\right)}\cdot\dfrac{3}{4\left(x-2\right)}\)
\(=\dfrac{2\left(6x^2-11x-3\right)}{x\left(2x-3\right)\cdot4\left(x-2\right)}\cdot3\)
\(=\dfrac{18x^2-33x-9}{2x\left(2x-3\right)\left(x-2\right)}\)
