Question

For what values of x is the rational expression below undefined?

Answer 1

Answer:

The correct options are D and F.

Step-by-step explanation:

The given expression is

$\frac{x+8}{x^2-2x-24}$

The given expression is undefined if the value of denominator is equal to 0.

Equate the denominator value equal to 0.

$x^2-2x-24=0$

The middle term can be written as -6x+4x.

$x^2-6x+4x-24=0$

$x(x-6)+4(x-6)=0$

$(x-6)(x+4)=0$

Equate each factor equal to 0.

$x-6=0\Rightarrow x=6$

$x+4=0\Rightarrow x=-4$

Therefore the given expression is undefined at x=6 and x=-4. Options D and F are correct.

Answer 2

The simplified form is (x+8)/ (x-6)(x+4).

In order for the expression to be undefined, the denominator must be equal to 0. Therefore you can set (x-6)(x+4)=0 so theerefore x=6 and x=-4