Question

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

Check all that apply.
x+8/x^2-2x-24
A. -6
B. -8
C. 8
D. 6
E. 4
F. -4

Answer 1

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

Answer 2

The correct options are D and F.

Explanation:

The given expression is

`(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.