f(x) = is negative if and only if
By taking factors of numerator and denominator, the function can be written as
The function will be negative if and only if one or three of the factors are negative.
When x < -5, all factors are negative. If -5 < x < - 2, only (x +5) is positive. If 3 < x < 9, only (x – 9) is negative.
Thus, f(x) = is negative if and only if -5 < x < -2 or 3 < x < 9