To find the non-permissible values for a rational expression, we need to identify the values of x that would make the denominator equal to zero. Since dividing by zero is undefined, these values are considered non-permissible.
In this case, the expression is (x^2 + x - 6) / (x^2 + x - 12).
To find the non-permissible values, we set the denominator equal to zero:
x^2 + x - 12 = 0.
Next, we need to factorize the quadratic equation to solve for x:
(x + 4)(x - 3) = 0.
Now, we can set each factor equal to zero and solve for x:
x + 4 = 0, x - 3 = 0.
Solving for x in each equation:
x = -4, x = 3.
Therefore, the non-permissible values for the given rational expression are x = -4 and x = 3.
So, the correct answer is d) x = 3 and x = -4.