Question 444042
find the vertical and horizontal asymptote of the function: x+5/x^2+4x+8
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If the degree of the numerator is less than the degree of the denominator, as in this case, the x-axis is the horizontal asymptote, that is, y=0

To find the vertical asymptotes, set the denominator=0, then solve for  x.
x^2+4x+8=0
solve by quadratic formula:
a=1, b=4,  c=8
x=[-4+-sqrt(4^2-4*1*8)]/2*1
x=(-4+-√-16)/2
This expression has two imaginary roots.
The denominator of the above expression can never be zero; for this reason, given function has no vertical asymptotes.