Remember: You cannot have three asymptotes at the same time. If the Horizontal Asymptote exists, the Oblique Asymptote doesn't exist. Also, #color (red) (H.A)# #color (red) (follow)# #color (red) (three)# #color (red) (procedures).# Let's say #color (red)n# = highest degree of the numerator and #color (blue)m# = highest degree of the denominator,#color (violet) (if)#:
#color (red)n color (green)< color (blue) m#, #color (red) (H.A => y = 0)#
#color (red)n color (green)= color (blue) m#, #color (red) (H.A => y = a/b)#
#color (red)n color (green)> color (blue) m#, #color (red) (H.A) # #color (red) (doesn't)# #color (red) (EE)#
Here, we have #(x +3)/(x^2 - 9)#
#color (red)n color (green)< color (blue) m#, so #color (red) (H.A EE)# #=> H.A: y = 0#
#x^2 - 9 = 0 => x = +- 3# are your vertical asymptotes #=> V.A : x = +-3#
I hope this is helpful :)
