Answer
$\lim\limits_{x\to\infty}\frac{3x-2}{2x+1}=\frac{3}{2}$
Work Step by Step
$$A=\lim\limits_{x\to\infty}\frac{3x-2}{2x+1}$$
Divide both numerator and denominator by $x$
$A=\lim\limits_{x\to\infty}\frac{\frac{3x-2}{x}}{\frac{2x+1}{x}}$
$A=\lim\limits_{x\to\infty}\frac{3-\frac{2}{x}}{2+\frac{1}{x}}$
$A=\frac{\lim\limits_{x\to\infty}(3-\frac{2}{x})}{\lim\limits_{x\to\infty}(2+\frac{1}{x})}$
$A=\frac{\lim\limits_{x\to\infty}3-\lim\limits_{x\to\infty}\frac{2}{x}}{\lim\limits_{x\to\infty}2+\lim\limits_{x\to\infty}\frac{1}{x}}$
$A=\frac{3-0}{2+0}$ (Theorem 5)
$A=\frac{3}{2}$
