Question

How do you find the asymptotes for `((x-3)(9x+4))/(x^2-4)`?

Answer 1

Vertical asymptote x=2, x=-2
Horizontal y=9

Explanation:

Equating denomnator =0 it is (x-2)(x+2)=0

The two vertical asymptotes are x=2 and x=-2. Next, dividing the numerator with denominator,
f(x)=`(9x^2 -23x -12)/(x^2-4) = 9+ (-23x +24)/(x^2-4)`

This gives y=9 as the horizontal asymptote.