Answer:
-5 < x < 6
Explanation:
You want to know the solution to (x -6)/(x +5) < 0.
Sign changes
The linear factors are zero at x=6 and x=-5. At each of these points, the function (x-6)/(x+5) changes sign.
When x > 6, the signs of both factors are positive, so the inequality is not satisfied. When x < -5, the signs of both factors are negative, so the inequality is not satisfied.
For values of x between -5 and +6, the signs of the factors are different, so the inequality is satisfied.
-5 < x < 6
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Additional comment
When the number of negative signs in a product or quotient is odd, the result will be negative. An even number of minus signs will result in a positive product or quotient. This relationship is used to solve rational and polynomial inequalities.
If the multiplicity of a factor is even, the sign does not change when x crosses its zero. For example, (x -1)² > 0 both for x < 1 and for x > 1.