# How do you find the vertical, horizontal and slant asymptotes of: y= (x+2)/(x^2-64)?

Jun 22, 2018

vertical asymptote = 8 and -8
horizontal asymptote = 0
slant asymptote = does not exist

#### Explanation:

• To work out the vertical asymptote we let the denominator = 0 and solve for x
${x}^{2} - 64 = 0$
${x}^{2} = 64$
$x = \pm \sqrt{64}$
$x = 8 , x = - 8$

• For the horizontal asymptote, since the degree of the denominator is greater than the degree of the numerator- that is, ${x}^{2} > x$, the horizontal asymptote is simply y = 0

• Lastly, to work out the slant asymptote, since the degree of the numerator is not greater than the degree of the denominator ( $x < {x}^{2}$) there is no slant asymptote.