College Algebra

Question

I need step by step how to solve this problem.

 

Find any vertical and horizontal asymtopes for:

 

X^2-2x-24/ x^2-9

 

*^= exponent

*/= Over (such as 2/4 would be 2 over 4)

Answer 1

(x^2-2x-24)/(x^2-9)

vertical asymptotes:

factor x^2-9

x^2-9=(x-3)(x+3)

vertical asymptotes are x=3 and x=-3 (the denominator can't be 0)

 

horizontal asymptotes:

both polynomials are the same degree, so divide the coefficients of the terms with the highest degrees

x^2=1x^2 so...

the horizontal asymptote is at y=1/1 or just y=1