How to find the asymptotes of the graph $y=\frac{x^2-5x-4}{x^2-5x+4}$? I just came across this question asking me to find the asymptotes of 
$$y=\frac{x^2-5x-4}{x^2-5x+4}$$
I typed this into my graphics calculator but I've never seen this type of graph before so this is something new. Currently studying functions. 
Would someone be able to explain to me thoroughly how to solve this problem and how to go about this type of questions in general?
Thank you!

$$y=\frac{x^2-5x-4}{x^2-5x+4}$$
Rewriting:
$$y=\frac{x^2-5x+4-8}{x^2-5x+4}$$
$$y=1-\frac8{x^2-5x+4}$$
So if you take the limit as x approaches infinity:
$$lim_{x\to\infty}(1- \frac8{x^2-5x+4})=1$$
So the curve will be pretty close to $y=1$ as x gets larger, so it is the horizontal asymptote
Then we need to see if the denominator of the fraction can get arbitrarily small, that is, if the denominator could be equal to 0.
Turns out; $$x^2-5x+4=(x-4)(x-1)$$
So when x approaches those $4$ or $1$, the value of y will tend to infinity. So $x=4$ and $x=1$ are the vertical asymptote
