Answer
$\lim\limits_{x \to \infty}\frac{2x-1}{3x+2} = \frac{2}{3}$
Work Step by Step
We look at the terms in the numerator and denominator with highest degree, as they will be the only terms with significance when x approaches infinity.
$\lim\limits_{x \to \infty}\frac{2x-1}{3x+2} = \lim\limits_{x \to \infty}\frac{2x}{3x} = \lim\limits_{x \to \infty}\frac{2}{3} = \frac{2}{3}$
