# How to find the asymptotes of f(x) = (x^2-1)/(2x^2 + 3x-2)?

Dec 25, 2015

-2 and -1/2 are the asymptotes

#### Explanation:

To find the asymptotes of an equation, think of values that cannot be a result of the function when it is substituted by many values.

In this case, since it is a fraction, 0 denominator is not possible cpbecause it will lead to undefine , so to find the asymptotes, find values that could make the denominator.

So let $2 {x}^{2} + 3 x - 2 = 0$

Then solve for x

$2 {x}^{2} + 3 x - 2 = 0$
$\left(2 x - 1\right) \left(x + 2\right) = 0$
$2 x - 1 = 0$
$x = \frac{1}{2}$
And

$x + 2 = 0$
$x = - 2$

So the asymptotes are -2 and $\frac{1}{2}$