Answer
slant asymptote $y=\frac{x}{2}-\frac{1}{4}$
vertical asymptotes $x=1$ and $x=\frac{1}{2}$
see graph.
Work Step by Step
1. Use long division as shown in the figure, we can get the quotient as $\frac{x}{2}-\frac{1}{4}$
which gives the slant asymptote as $y=\frac{x}{2}-\frac{1}{4}$
2. The vertical asymptote can be identified by factoring the denominator
$2x^2+x-1=(2x-1)(x+1)$, thus the vertical asymptotes are $x=-1$ and $x=\frac{1}{2}$
3. We can graph the function as shown in the figure together with the asymptotes.
