Question

Find all numbers that must be excluded from the domain of the rational expression.

x-2

x2+9x+8

(Use a comma to separate answers as needed.)

Type the values for which the rational expression is undefined. Select the correct choice below and fill in any answer boxes within your choice.

O A.

OB. The rational expression is defined for all real numbers.

Answer 1

To find the values that must be excluded from the domain of the rational expression \(\frac{x-2}{x^2 + 9x + 8}\), we need to identify when the denominator is zero.

First, we will set the denominator equal to zero and solve for \(x\):

1. Set the denominator equal to zero:
\[
x^2 + 9x + 8 = 0
\]

2. Factor the quadratic expression:
\[
x^2 + 9x + 8 = (x + 1)(x + 8)
\]

3. Set each factor to zero:
\[
x + 1 = 0 \quad \Rightarrow \quad x = -1
\]
\[
x + 8 = 0 \quad \Rightarrow \quad x = -8
\]

Thus, the values that must be excluded from the domain are \(x = -1\) and \(x = -8\).

So, the answer is:
\[
-1, -8
\]

This means that the rational expression \(\frac{x-2}{x^2 + 9x + 8}\) is undefined for \(x = -1\) and \(x = -8\).