## Precalculus (6th Edition) Blitzer

For the limit $\lim_{x\to4}\frac{(x+4)(x-4)}{x-4}$, when $x$ approaches $4$, it can get really close to but never be $4$. That is, $x\ne4$ or $x-4\ne0$ is true. Thus, we can divide the numerator and the denominator by $x-4$.