Solving Limits (Rationalization)

Watch this video on finding limits algebraically. Be warned that removing $x-4$ from the numerator and denominator in Step 4 of this video is only legal inside this limit. The function $\frac{x - 4}{x - 4}$ is not defined at $x = 4$; however, when $x$ is not 4, it simplifies to 1. Because the limit as $x$ approaches 4 depends only on values of $x$ different from 4, inside that limit $\frac{x - 4}{x - 4}$ and 1 are interchangeable. Outside that limit, they are not! However, this kind of cancellation is a key technique for finding limits of algebraically complicated functions.