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

Question

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 \(x = -8\).