Answer
False
Work Step by Step
In this case, we'd use the property of limit of a sum (or a difference), that is:
$\lim\limits_{a \to b} [f(x)\pm g(x)] =\lim\limits_{a \to b} f(x) \pm \lim\limits_{a \to b} g(x).$ But, the functions $f(x)=\frac{2x}{x-4}$ and $g(x)=\frac{8}{x-4}$ are not continuous in the point x=4, because we are going to have an indeterminate expression. Thus, we can't use the property of limits.
