Answer
Slant asymptote: $y=2x$
Vertical asymptotes: $x=-1$ and $x=1$
See graph.
Work Step by Step
1. Factor the denominator as $(x+1)(x-1)$ and use synthetic divisions as shown in the figure,
2. Based on the division results, we get $r(x)=2x+\frac{4}{(x+1)(x-1)}$
3. We can identify the slant asymptotes as $y=2x$
4. The vertical asymptotes can be found as $x=-1$ and $x=1$
5. The graph of the function is shown in the figure.
