Final answer:
The expression is undefined for x = 9 and x = -4.
Step-by-step explanation:
This expression is a quadratic equation of the form at² + bt + c = 0, where the constants are given as a = 4, b = -8, and c = -36.
To determine for which values of c the expression is undefined, we need to find the values of x that make the denominator zero in the expression 4x - 8 / (x² - 5x - 36).
In this case, the expression is undefined for any value of x that makes the denominator zero.
We can find these values by setting the denominator equal to zero and solving the resulting quadratic equation.
Setting the denominator equal to zero, we have x² - 5x - 36 = 0.
We can factorize this quadratic equation as (x - 9)(x + 4) = 0. Setting each factor equal to zero, we find x - 9 = 0 and x + 4 = 0.
Solving for x, we get x = 9 and x = -4.
Therefore, the expression is undefined for x = 9 and x = -4, since these values would make the denominator zero.