We want to find the oblique asymptote for the following function
[tex]f(x)=\frac{x^3-7x-6}{x^2-2x-15}[/tex]To find the oblique asymptote, we just need to effectuate the division and analyse its behavior as it goes to infinity.
Doing the division, we have
[tex]\frac{x^3-7x-6}{x^2-2x-15}=x+2+\frac{12x+24}{x^2-2x-15}[/tex]The rational term approaches 0 as the variable approaches infinity.
Thus, the oblique asymptote is y = x + 2