# How do you find the asymptotes for f(x) = (x+1) / (x^2 +3x - 4) ?

Jan 25, 2016

$x = - 4$ and $x = + 1$

#### Explanation:

Vertical asymptotes
substitute values of x that will make the denominator 0.
to do that you must factor, the denominator to obtain
$\textcolor{w h i t e}{\text{XX}} \left(x + 4\right) \left(x - 1\right)$,
then the values that would make this denominator 0 are
$\textcolor{w h i t e}{\text{XX}} - 4 \mathmr{and} + 1$.

therefore, the equations of the asymptotes are,
$\textcolor{w h i t e}{\text{XX}} x = - 4 \mathmr{and} x = 1$.
graph{(x+1)/(x^2+3x-4) [-6.244, 6.243, -3.12, 3.123]}

Note there are no horizontal asymptotes.