$$\frac{4x}{3x^{2}-x-2}-\frac{x-2}{3x^{2}-x-2}$$
$\frac{1}{x-1}$
$$\frac{4x-\left(x-2\right)}{3x^{2}-x-2}$$
$$\frac{4x-x+2}{3x^{2}-x-2}$$
$$\frac{3x+2}{3x^{2}-x-2}$$
$$\frac{3x+2}{\left(x-1\right)\left(3x+2\right)}$$
$$\frac{1}{x-1}$$
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$\frac{3}{3x-3}$
