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

Jan 18, 2018

Vertical asymptote at $x = 1$

Oblique asymptote at $y = x + 1$

#### Explanation:

A vertical asymptote occurs where the denominator is equal to $0$.

So we have:

$x - 1 = 0 \to x = 1$

So a vertical asymptote will occur where $x = 1$.

The degree of the numerator is greater than the degree of the denominator so the function will not have horizontal asymptotes but will have oblique ones. To find them: we must split the fraction up like so:

${x}^{2} / \left(x - 1\right) = x + \frac{x}{x - 1} = x + 1 + \frac{1}{x - 1}$

So for very large values of $x$ the fraction term will become insignificantly small and the function will approach the oblique asymptote: $y = x + 1$.