Question 1164558
your inequality is:


(x^2 - x - 12)/(x^2 + x - 6) > 0


factor these quadratics to get:


(x-4)*(x+3)/((x-2)*(x+3)) > 0


the (x+3) in the numerator and the denominator cancel out and you are left with:


(x-4)/(x-2) > 0


this will be positive when x is greater than 4 or when x is smaller than 2


it till be negative when x is > 2 and < 4.


when x is greater than 4, you have a positive numerator divided by a positive denominator which results in a positive number.


when x is less than 2, you have a negative numerator divided by a negative denominator which results in a positive number.


when x is greater than 2 and less than 4, you have a negative numerator divided by a positive denominator which results in a negative number.


this can be seen in the following graph.


<img src = "http://theo.x10hosting.com/2020/090904.jpg" >


the shaded area is when the resulting number is positive.
the non-shaded area is when the resulting number if negative.