Question 892661
Perform the polynomial division.  You should likely find a remainder, which may become increasingly small as x tends to plus or minus infinity, meaning that the quotient without the remainder will be the slant asymptote.


You have a rational expression function.  Divide {{{x^3-1}}}  by  {{{x^2-9}}}.  
The quotient found is {{{highlight_green(x+(9x-1)/(x^2-9))}}}.
Notice the degree of the numerator of the remainder is smaller than the degree of the denominator of the remainder.  As x goes to either extreme, the quotient gets closer to {{{highlight(y=x)}}}, which is the slant asymptote.


Compare with the graph:


{{{graph(300,300,-15,15,-15,15,(x^3-1)/(x^2-9))}}}


,and then showing the included line for the asymptote,
{{{graph(300,300,-15,15,-15,15,(x^3-1)/(x^2-9),x)}}}