Solve for x
x\in \left(-\infty,-2\right)\cup \left(6,\infty\right)
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x+2>0 6-x<0
For the quotient to be negative, x+2 and 6-x have to be of the opposite signs. Consider the case when x+2 is positive and 6-x is negative.
x>6
The solution satisfying both inequalities is x>6.
6-x>0 x+2<0
Consider the case when 6-x is positive and x+2 is negative.
x<-2
The solution satisfying both inequalities is x<-2.
x>6\text{; }x<-2
The final solution is the union of the obtained solutions.
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