for what value of x is the rational expression below undefined? x+8/x^2 -2x-24

First step: Factor the expression.
(x + 8) / (x - 6)(x + 4)
Set each factor of the denominator equal to zero.
x - 6 = 0 x + 4 = 0
add 6 to both sides subtract 4 from both sides
x = 6 x = -4
The function would be undefined if x = 6 or x = -4

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keshavgandhi04 keshavgandhi04 · Answer 2 · 2021-12-20T11:42:26+01:00

The value of x at which the given rational function is undefined is -4 and 6 and this can be determined by factorizing the denominator.

Given :

Rational Expression -- [tex]\dfrac{x+8}{x^2-2x-24}[/tex]

The following steps can be used in order to determine the value of x is the rational expression given undefined:

Step 1 - Write the rational expression.

[tex]\dfrac{x+8}{x^2-2x-24}[/tex]

Step 2 - In the rational function, the denominator is not equal to zero.

[tex]x^2-2x-24\neq 0[/tex]

Factorize the above equation.

[tex]x^2-6x+4x-24\neq 0[/tex]

[tex]x(x-6)+4(x-6)\neq 0[/tex]

[tex](x-6)(x+4)\neq 0[/tex]

Step 3 - So, the value of x at which the given rational function is undefined is -4 and 6.

For more information, refer to the link given below:

https://brainly.com/question/15324782