Question

How do you find vertical, horizontal and oblique asymptotes for `(X^2)/( X-1)`?

Answer 1

Vertical asymptote of `(X^2)/(X-1)` is given by `x-1=0`.
and oblique asymptote is `y=x`

Explanation:

The vertical asymptotes of `(X^2)/(X-1)` are given by zeros of denominator i.e. `x-1=0`.

As the degree of numerator is just one higher than that of denominator, there is no horizontal asymptote, but we do have a slant asymptote given by `y=(X^2)/X=X`.

The slant asymptote is given by `y=x`

graph{(x^2)/(x-1) [-15, 15, -15, 15]}