We cannot do crossing over
#x/(x-2)-2>0#
#(x-2(x-2))/(x-2)>0#
#(4-x)/(x-2)>0#
Let #f(x)=(4-x)/(x-2)#
The domain of #f(x)# is #D_f(x)=RR-{2}#
Now we can do our sign chart
#color(white)(aaaa)##x##color(white)(aaaa)##-oo##color(white)(aaaa)##2##color(white)(aaaa)##4##color(white)(aaaa)##+oo#
#color(white)(aaaa)##x-2##color(white)(aaaa)##-##color(white)(a)##∥##color(white)(a)##+##color(white)(aa)##+#
#color(white)(aaaa)##4-x##color(white)(aaaa)##+##color(white)(a)##∥##color(white)(a)##+##color(white)(aa)##-#
#color(white)(aaaa)##f(x)##color(white)(aaaaa)##-##color(white)(a)##∥##color(white)(a)##+##color(white)(aa)##-#
Therefore,
#f(x)>0# when #x in ] 2,4 [ #