How do you find the horizontal asymptote for f(x)= (3e^(x))/(2-2e^(x))?

##y=0##
##y=-3/2##
To find any horizontal we have to evaluate:
##lim_(x rarr+-oo)f(x)##
if the limits are finite then they are horizontal asymptotes
##lim_(x rarr-oo)f(x)=lim_(x rarr-oo)3/2(e^x/(1-e^x))=##
##3/2lim_(x rarr-oo)(e^x/(1-e^x))~~3/2lim_(x rarr-oo)e^x/1=3/2*0=0##
##:. y=0## is a horizontal asymptote for ##x rarr-oo##
##lim_(x rarr+oo)f(x)=lim_(x rarr+oo)3/2(e^x/(1-e^x))=##
##3/2lim_(x rarr+oo)(e^x/(1-e^x))~~3/2lim_(x rarr+oo)(e^x/-e^x)=##
##=3/2*(-1)=-3/2##
##:. y=-3/2## is a horizontal asymptote for ##x rarr+oo##
graph{(3/2)*((e^x)/(1-e^x)) [-10 10 -5 5]}