Solve for x
x\in \left(-\infty,-3\right)\cup \left(1,\infty\right)
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x+3<0 x-1<0
For the quotient to be positive, x+3 and x-1 have to be both negative or both positive. Consider the case when x+3 and x-1 are both negative.
x<-3
The solution satisfying both inequalities is x<-3.
x-1>0 x+3>0
Consider the case when x+3 and x-1 are both positive.
x>1
The solution satisfying both inequalities is x>1.
x<-3\text{; }x>1
The final solution is the union of the obtained solutions.
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