# How do you find the asymptotes for (2x^2 - x - 38) / (x^2 - 4)?

Feb 3, 2016

vertical asymptotes at x = ± 2

horizontal asymptote at y = 2

#### Explanation:

As the denominator of a rational function tends to 0 there
will be a vertical asymptote.

solve $\left({x}^{2} - 4\right) = 0$

$\left(x - 2\right) = 0 \mathmr{and} \left(x + 2\right) = 0$ hence vertical asymptotes at  x = ± 2

[horizontal asymptotes occur when  lim_(x→±∞) f(x) → 0]

when the degree of the numerator and denominator are equal

the equation can be found by taking the ratio of
and so $y = \frac{2}{1} \Rightarrow y = 2$