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