What values make the inequality x+6/6-x true?

the correct question is
What values make the inequality (x+6)/(6-x)<0 true?

we know that

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
(x+6) < 0  and (6-x) > 0--------> case 2

case 1
(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,∞)