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