f(x)=(x-5)(x+6)/(x-3)
Check regions:
x=(-inf,-6) (-)(-)/(-)<0 -> f(x)<0, so NOT in solution set
x=-6, f(-6)=0 -> x=-6 in solution set <====================
x=(-6,3) (-)(+)/(-) >0 -> f(x) >0 so in solution set <==========
x=3 f(x) undefined, so NOT in solution set
x=(3,5) (-)(+)/(+) <0 so NOT in solution set
x=5 f(5)=0 -> x=5 in solution set <=====================
to sum up,
S={[-6,3),5}
