The correct question is <span>What values make the inequality (x+6)/(6-x)<0 true?
we know that </span> <span>the denominator cannot be zero; so (6-x)------------> will be 0 if x=6
the inequality is true when (x+6) > 0 and (6-x) < 0--------> case 1 or </span>(x+6) < 0 and (6-x) > 0--------> case 2 <span> case 1 </span>(x+6) > 0 and (6-x) < 0 (x+6) > 0 --------------> x> -6 (6-x) < 0 ----------------> x> 6 solution--------> (6,∞)
case 2 (x+6) < 0 and (6-x) > 0 (x+6) < 0 --------------> x< -6 (6-x) > 0 ----------------> x < 6 solution--------> (-∞,-6)
the answer is the values that makes the inequality true are (-∞,-6) ∩ (6,∞)