[tex]f(x)=\frac{x^2-4x+8}{x+2}[/tex]
The polynomial in the numerator is of a higher degree (2) than the polynomial in the denominator (1), so there is an oblique asymptote.
To find the asymptote, divide the numerator by the denominator. The result, without the remainder, will be the equation of the asymptote.
Look at the picture.
The oblique asymptote is [tex]y=x-6[/tex].
