Question

Solve the inequality and express your answer in interval notation. (x - 5)(x+6)/(x-3) >= 0

Answer 1

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}