# What is the oblique asymptote of f(x)=(x^2+x-2)/(x+1)?

Oct 18, 2015

The oblique asymptote is $y = x$
$f \left(x\right) = \frac{{x}^{2} + x - 2}{x + 1} = \frac{x \left(x + 1\right) - 2}{x + 1} = x - \frac{2}{x + 1}$
As $x \to \pm \infty$, $- \frac{2}{x + 1} \to 0$.
So $f \left(x\right)$ is asymptotic to the line $y = x$.