Question 965956
Arithmetic mistake in your finding y=0.  Otherwise, your asymptote judgement is good.


{{{(0-4)/((0^2)-4)}}}


{{{-4/(-4)}}}


{{{1}}}


{{{graph(300,300,-10,10,-10,10,(x-4)/((x^2)-4))}}}



A different view:
{{{graph(300,300,0,20,-10,10,(x-4)/((x^2)-4))}}}


Another view:
{{{graph(300,300,-20,0,-10,10,(x-4)/((x^2)-4))}}}