Cancelling Common Factors
When you have a function such that $f(x) = \frac{P(x)}{Q(x)}$ where $P(x)$ and $Q(x)$ are polynomials and $P(a) = Q(a) = 0$ where a is in the domain of x, we can solve the limit $\lim_{x\to a}$ by cancelling out a common factor between $P$ and $Q$. We know that there must be a common factor since they both have the root a so the common factor is $(x - a)$. We can calculate the other factor of the polynomial by doing polynomial division.