What is the vertical and horizontal asymptotes of

Question

..

3x
_________
x^2-3x-10

Answer 1

vertical asymptotes occur when the denominator is zero, so
x^2 - 3x - 10 = 0
(x-5)(x+2) = 0
x = 5 or x = -2 are vertical asymtotes

let x ---> ∞
so 3x/(x^2 - 3x-10) ---> 0

the horizontal asymptote is y = 0 , which is the x-axis