Question

find any numbers for which the rational expression is undefined.
$\frac{3x^{2}+9}{x^{2}-2x-8}$
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the rational expression is undefined when x is .
(type an integer or a simplified fraction. use a comma to separate answers as needed.)
b. there are no values of x for which the rational expression is undefined.

Explanation:

Step1: Set denominator equal to 0

$x^2 - 2x - 8 = 0$

Step2: Factor the quadratic equation

$(x - 4)(x + 2) = 0$

Step3: Solve for x

$x - 4 = 0 \implies x = 4$; $x + 2 = 0 \implies x = -2$

Answer:

A. The rational expression is undefined when x is $4, -2$.