Question 818315
If the function is
f(x) = x/x^2+4={{{x/x^2+4=1/x+4}}} {{{graph(300,300,-5,5,-5,15,x/x^2+4)}}}
there is a vertical asymptote, {{{x=0}}}.
 
If the function is
f(x) = x/(x^2+4)={{{x/(x^2+4)}}} {{{graph(300,300,-20,20,-0.5,0.5,x/(x^2+4))}}}
there is no vertical asymptote,
because the denominator, {{{x^2+4}}} ,
is not zero for any real value of {{{x}}} .