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

Apr 16, 2016

Vertical asymptote of $\frac{{X}^{2}}{X - 1}$ is given by $x - 1 = 0$.
and oblique asymptote is $y = x$

#### Explanation:

The vertical asymptotes of $\frac{{X}^{2}}{X - 1}$ 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 $y = \frac{{X}^{2}}{X} = X$.

The slant asymptote is given by $y = x$

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