We cannot do crossing over
#x/(x-3)<=-8/(x-6)#
We rearrange and factorise the inequality
#x/(x-3)+8/(x-6)<=0#
#(x(x-6)+8(x-3))/((x-3)(x-6))<=0#
#(x^2-6x+8x-24)/((x-3)(x-6))<=0#
#(x^2+2x-24)/((x-3)(x-6))<=0#
#((x-4)(x+6))/((x-3)(x-6))<=0#
Let #f(x)=((x-4)(x+6))/((x-3)(x-6))#
We can build the sign chart
#color(white)(aaaa)##x##color(white)(aaaa)##-oo##color(white)(aaaa)##-6##color(white)(aaaaaaa)##3##color(white)(aaaaa)##4##color(white)(aaaaaaa)##6##color(white)(aaaa)##+oo#
#color(white)(aaaa)##x+6##color(white)(aaaaa)##-##color(white)(aaaa)##+##color(white)(aaaa)##||##color(white)(aa)##+##color(white)(aa)##+##color(white)(aaaa)##||##color(white)(aa)##+#
#color(white)(aaaa)##x-3##color(white)(aaaaa)##-##color(white)(aaaa)##-##color(white)(aaaa)##||##color(white)(aa)##+##color(white)(aa)##+##color(white)(aaaa)##||##color(white)(aa)##+#
#color(white)(aaaa)##x-4##color(white)(aaaaa)##-##color(white)(aaaa)##-##color(white)(aaaa)##||##color(white)(aa)##-##color(white)(aa)##+##color(white)(aaaa)##||##color(white)(aa)##+#
#color(white)(aaaa)##x-6##color(white)(aaaaa)##-##color(white)(aaaa)##-##color(white)(aaaa)##||##color(white)(aa)##-##color(white)(aa)##-##color(white)(aaaa)##||##color(white)(aa)##+#
#color(white)(aaaa)##f(x)##color(white)(aaaaaa)##+##color(white)(aaaa)##-##color(white)(aaaa)##||##color(white)(aa)##+##color(white)(aa)##-##color(white)(aaaa)##||##color(white)(aa)##+#
Therefore,
#f(x)<=0# when # x in [-6,3[ uu [4,6 [#