Solve for x
x\in \left(-1,1\right)
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x+1<0 1-x<0
For the quotient to be positive, x+1 and 1-x have to be both negative or both positive. Consider the case when x+1 and 1-x are both negative.
x\in \emptyset
This is false for any x.
1-x>0 x+1>0
Consider the case when x+1 and 1-x are both positive.
x\in \left(-1,1\right)
The solution satisfying both inequalities is x\in \left(-1,1\right).
x\in \left(-1,1\right)
The final solution is the union of the obtained solutions.
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