Answer:
Step-by-step explanation:
In order to be undefined, the fraction must have the denominator equal to 0, therefore we need to solve the equation
[tex]x^2 -4x - 12 = 0\\[/tex]
This is a second degree equation, and we can re-write it to
[tex](x-6)(x+2) = 0[/tex]
We notice that the solution to be composed of 2 values:
x = 6
and
x = -2
Therefore the set of values of x for which the said expression is undefined is
S={-2, 6}
Alternatively, if you don't notice how to re-write it factored, you can use the 2nd degree equation solving algorithm:
[tex]\Delta = (-4)^2 - 4\cdot1\cdot(-12) = 16+48 = 64\\x_1 = \frac{-(-4)-\sqrt{64} }{2\cdot1} = -2\\x_1 = \frac{-(-4)+\sqrt{64} }{2\cdot1} = 6[/tex]
