Question 378269
 {{{drawing(300,300,-10,10,-10,10,blue(line(-3,10,-3,-10)),graph(300,300,-10,10,-10,10,0,(x^2+4x-5)/(x^2+8x+15)))}}}
 .
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Why?
{{{f(x)=(x^2+4x-5)/(x^2+8x+15)}}}
{{{f(x)=((x+5)(x-1))/((x+3)(x+5))}}}
 {{{highlight(f(x)=(x-1)/(x+3))}}}
Now you see the reason for the vertical asymptote only at {{{x=-3}}}.