# How do you determine the limit of (x+4)/(x-4) as x approaches 4+?

Jul 11, 2016

${\lim}_{x \to {4}^{+}} \frac{x + 4}{x - 4} = \infty$

#### Explanation:

${\lim}_{x \to {4}^{+}} \left(x + 4\right) = 8$

$\therefore 8 {\lim}_{x \to {4}^{+}} \frac{1}{x - 4}$

As ${\lim}_{x \to {4}^{+}} \left(x - 4\right) = 0$ and all points on the approach from the right are greater than zero, we have:

${\lim}_{x \to {4}^{+}} \frac{1}{x - 4} = \infty$

$\implies {\lim}_{x \to {4}^{+}} \frac{x + 4}{x - 4} = \infty$