# How do you find the asymptotes of f(x)= (x^2+1)/(x+1)?

Oct 6, 2015

$y = x - 1$ is an oblique asymptote.
$\frac{{x}^{2} + 1}{x + 1} = x - 1 + \frac{2}{x + 1}$ $\text{ }$(by division)
So, as $x$ increases or decreases without bound, the difference between $f \left(x\right)$ and the $y$ value of $y = x - 1$ approaches $0$.
So the graph of $f \left(x\right)$ approaches the line $y = x - 1$.