Let #f(x)=(x^2-4)/(3-x)=((x-2)(x+2))/(3-x)#
The domain is #D_f=RR-{3} #
Let's do the sign chart
#color(white)(aaaaa)##x##color(white)(aaaa)##-oo##color(white)(aaaaa)##-2##color(white)(aaaaa)##2##color(white)(aaaaa)##3##color(white)(aaaaa)##+oo#
#color(white)(aaaaa)##x+2##color(white)(aaaaa)##-##color(white)(aaaaaa)##+##color(white)(aaaa)##+##color(white)(aaa)##+#
#color(white)(aaaaa)##x-2##color(white)(aaaaa)##-##color(white)(aaaaaa)##-##color(white)(aaaa)##+##color(white)(aaa)##+#
#color(white)(aaaaa)##3-x##color(white)(aaaaa)##+##color(white)(aaaaaa)##+##color(white)(aaaa)##+##color(white)(aaa)##-#
#color(white)(aaaaa)##f(x)##color(white)(aaaaaa)##+##color(white)(aaaaaa)##-##color(white)(aaaa)##+##color(white)(aaa)##-#
Therefore, #f(x)>=0#
when #x in] -oo,-2 ] uu [2, 3[#
graph{(x^2-4)/(3-x) [-34.51, 30.44, -18.83, 13.64]}