How do you find the vertical, horizontal and slant asymptotes of: #(x^2 - 5)/( x+3)#?

1 Answer
Oct 26, 2016

Answer:

The vertical asymptote is #x=-3#
The slant asymptote is #y=x-3#
There is no horizontal asmptote

Explanation:

The domain of the function is #RR-(-3)#
As we cannot divide by 0

As the degree of the numerator is greater than the degree of the denominator, we would expect a slant asymptote. So we make a long division

#x^2##color(white)(aaaa)##-5##∣##x+3#
#x^2+3x##color(white)(aa)##∣##x-3#
#0-3x-5#
#color(white)(aa)##-3x-9#
#color(white)(aaaaa)##0+4#

So we can rewrite the function
#(x^2-5)/(x+3)=x-3+4/(x+3)#

So the slant asymptote is #y=x-3#