RootMath: "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.