Applying division signal rules, from the graphs of both functions, it is found that the solution of the inequality is:
[tex]x \in [-3,-1) \cup [2,4)[/tex]
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A fraction, which represents a division, is negative if the numerator and the denominator have different signals. Thus, to solve this inequality, we have to study the signals of the numerator and the denominator.
The numerator is: [tex]f(x) = x^2 + x - 6[/tex]
- It is the first graph appended at the end of this answer.
- From the graph, we have that it is negative or zero on [-3,2], and positive on the rest of the interval.
The denominator is: [tex]g(x) = x^2 - 3x - 4[/tex]
- It is the second graph appended at the end of this answer.
- The denominator cannot be zero, so we consider only the interval (-1,4), in which it is negative.
- Numerator positive, denominator negative: On interval [2,4).
- Denominator positive, numerator negative. On interval [-3,-1).
Thus, the solution is:
[tex]x \in [-3,-1) \cup [2,4)[/tex]
A similar problem is given at https://brainly.com/question/14361489
