Answer
$\lim\limits_{x \to 2}\frac{f(x)}{g(x)} = -1.5$
Work Step by Step
$\lim\limits_{x \to 2}\frac{f(x)}{g(x)} = \lim\limits_{x \to 2}\frac{1.5(x-2)}{2-x} = \frac{0}{0}$
We can use L'Hospital's Rule:
$\lim\limits_{x \to 2}\frac{f'(x)}{g'(x)} = \lim\limits_{x \to 2}\frac{1.5}{-1} = -1.5$
$\lim\limits_{x \to 2}\frac{f(x)}{g(x)} = -1.5$
