Question

How do you find the asymptotes for `{-9 x^3 - 9 x^2 + 28 x + 9 }/{3 x^2 + 6 x + 2}`?

Answer 1

Oblique asymptotes y= -3x +3

Vertical asymptotes `x=(-3+-sqrt 3)/3`

Explanation:

On division the given expression appears like this

(-3x +3)+ `(16x+3)/(3x^2 +6x +2)`

Oblique asymptote is given by y=-3x+3

Vertical asymptotes are given by `3x^2 +6x+2=0`, that is `x= (-6+- sqrt(36-12))/6`

`x=(-3+-sqrt 3)/3`