Finding limits when given $2$ different limits.

Question

Let $\lim\limits_{x\to -1} f(x) = 8$ and $\lim\limits_{x\to -1} g(x) =-4$. Find $\lim\limits_{x\to -1} \dfrac{f(x)}{g(x)}$.

Answer Choices are:

A. $-2$

B. $12$

C. $-1/2$

D. $-1$

I started out trying to solve this problem by attempting to use a derivative formula which just overcomplicated the problem and did not lead me to any of the potential answer choices.

I was struggling with this problem as I did not understand the limit laws and upon further review I understood them well enough to realize that I should have just simply plugged in my $f(x)$ and $g(x)$ values to get my final answer of $-2$.

Is this okay?

Answer 1

hint: $\lim\limits_{x\to c} \frac{f(x)}{g(x)}=\frac{L}{H}$ where $\lim_{x\to c}f(x)=L$ and provided $\lim_{x\to c}g(x)=H\not = 0$

Answer 2

Using the limit rules and the help provided by other people I was able to determine that the final answer is -2

I also realize now that I way over thinking this question. It has been a long day of math I am sorry for asking such an obvious one when the answer was as right in front of me in the form of basic math.