q(x)=3x^2-11x-4/5x^2-16x-16
what are the
oblique
horizontal
vertical asyptote
I assume you mean
q(x) = (3x^2 - 11x - 4)/(5x^2 - 16x - 16)
then
q(x) = (3x+1)(x-4)/( (5x+4)(x-4) )
= (3x+1)/(5x+4) , x ≠ 4
vertical asymptote : x = -4/5
horizontal ... : y = 3/5
no oblique
there is a "hole" at (4, 13/24)