Solve for x
x\in \left(-\infty,-2\right)\cup \left(3,\infty\right)
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x+2<0 2x-6<0
For the quotient to be positive, x+2 and 2x-6 have to be both negative or both positive. Consider the case when x+2 and 2x-6 are both negative.
x<-2
The solution satisfying both inequalities is x<-2.
2x-6>0 x+2>0
Consider the case when x+2 and 2x-6 are both positive.
x>3
The solution satisfying both inequalities is x>3.
x<-2\text{; }x>3
The final solution is the union of the obtained solutions.
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