Let #f(x)=(1-x)/(x-9)#

The domain of #f(x)# is #D_f(x)=RR-{9}#

We build a sign chart

#color(white)(aaaa)##x##color(white)(aaaa)##-oo##color(white)(aaaa)##1##color(white)(aaaaaaaa)##9##color(white)(aaaaaaa)##+oo#

#color(white)(aaaa)##1-x##color(white)(aaaa)##+##color(white)(aaaa)##-##color(white)(aaaa)##||##color(white)(aaaa)##-#

#color(white)(aaaa)##x-9##color(white)(aaaa)##-##color(white)(aaaa)##-##color(white)(aaaa)##||##color(white)(aaaa)##+#

#color(white)(aaaa)##f(x)##color(white)(aaaaa)##-##color(white)(aaaa)##+##color(white)(aaaa)##||##color(white)(aaaa)##-#

Therefore,

#f(x)>=0#, when #x in [1, 9[#