Answer
vertical asymptote $x=0$,
horizontal asymptote $none$,
oblique asymptote $none$.
Work Step by Step
Step 1. Factor the function $G(x)=\frac{x^4-1}{x^2-x}=\frac{(x^2+1)(x+1)(x-1)}{x(x-1)}=\frac{(x^2+1)(x+1)}{x}, (x\ne1)$,
Step 2. we can find the vertical asymptote $x=0$,
Step 3. we can find the horizontal asymptote $none$,
Step 4. we can find the oblique asymptote $none$.
