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