Answer
False
Work Step by Step
"Difference Law: The limit of a difference is the difference of the limits"
$\lim\limits_{x\to a}[f(x)-g(x)] = \lim\limits_{x \to a}f(x) -\lim\limits_{x \to a}g(x)$
If the individual limits of each function exist.
You cannot subtract a limit which does not exist.
Thus the statement:
$\lim\limits_{x \to 4}[\frac{2x}{x-4}-\frac{8}{x-4}] = \lim\limits_{x \to 4}\frac{2x}{x-4} - \lim\limits_{x \to 4}\frac{8}{x-4}$
Is not true because the individual limits diverge (do not exist)
