When solving limits you might get a final answer that looks correct, but it might not work sometimes

If you end up with a limit's answer in one the 7 forms below, you are NOT at the final answer

$$ \frac{0}{0}, \frac{\infty}{\infty},\infty - \infty, 0^0, 0 \cdot \infty, 1^{\infty}, \infty^0$$

If you do encounter one of these answers, you need to apply some sort of techniques to get rid of it

Here's an example of why $\frac{0}{0}$ is not an acceptable answer

Observe the two limits below

$$\begin{align} \lim_{x \to 0}\frac{\sin(x)}{x} &= 1 \\ \lim_{x \to 3}\frac{x^2 + 2x - 15}{x - 3} &= 8 \\ \end{align}$$

If you used direct substituion, you would get $\frac{0}{0}$ for both, even though the actual answers are differnet