Question 895387
That rational equation has no horizontal asymptotes.  Notice x unbounded approaches either negative infinity or positive infinity, based on y approaching {{{x^2/x}}}.


Just to be more certain in possible vertical asymptotes, factorize the numerator if possible.
(x+3)(x+4)-----------the numerator.
NO vertical asymptote, because {{{y=((x+3)(x+4))/(x+4)}}}
{{{y=((x+3)cross((x+4)))/cross((x+4))}}}
{{{y=x+3}}}
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Your rational equation is the line but MISSING x=-4.  There is no included point at x=-4.  You can call this a hole in the line.  (This cannot be seen well on most graphs produced through software, but you can represent what you want in a manually drawn graph or sketch.)


No real use in looking for slant asymptote, since the rational equation is already a line  (missing one point.)