Solve for x
x\in \left(-6,6\right)
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x+6>0 x-6<0
For the quotient to be negative, x+6 and x-6 have to be of the opposite signs. Consider the case when x+6 is positive and x-6 is negative.
x\in \left(-6,6\right)
The solution satisfying both inequalities is x\in \left(-6,6\right).
x-6>0 x+6<0
Consider the case when x-6 is positive and x+6 is negative.
x\in \emptyset
This is false for any x.
x\in \left(-6,6\right)
The final solution is the union of the obtained solutions.
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