Solve for x
x\in \left(-\infty,-9\right)\cup \left(-7,\infty\right)
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x+7<0 x+9<0
For the quotient to be positive, x+7 and x+9 have to be both negative or both positive. Consider the case when x+7 and x+9 are both negative.
x<-9
The solution satisfying both inequalities is x<-9.
x+9>0 x+7>0
Consider the case when x+7 and x+9 are both positive.
x>-7
The solution satisfying both inequalities is x>-7.
x<-9\text{; }x>-7
The final solution is the union of the obtained solutions.
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