## 3psilon 3 years ago Help finding ALL asymtotes

1. 3psilon

of $y = \frac{ x^2 - 3x + 2 }{ x^{2}-1 }$

2. josiahh

$((x-1)(x-2))/((x-1)(x+1))$ $(x-2)/(x+1)$ you have vertical asymptote at x=-1 horizontal asymptotes at negative infinity and positive infinity y=1 is your horizontal asymptote for both infinities x=-1 is your only vertical one because you canceled out the (x-1) factor

3. 3psilon

I'm not really understanding the horizontal asymtote part :(

4. josiahh

you take limit as x approaches infinity and negative infinity. when you do that, you get 1. limit x approaches negative infinity = limit x approaches infinity =1

5. 3psilon

Do you always do that to find the horizontal asymtote ?

6. josiahh

yea. horizontal retricemptotes describe the behavior of the graph as x increases

7. 3psilon

@josiahh Doing it algebraically I'm not so good with limits So can you show me algebraically how the limit = 1 please?

8. josiahh

when you are taking limits at infinity, you look at the degree of the polynomials in the denominator and the numerator

9. 3psilon

Ohhhh and if they are equal its Coeffcient over coeffcient?

10. josiahh

yea that rule...

11. 3psilon

Thank YOU!

12. josiahh

welcome