Question

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

\\\frac{x - 5}{x^2 + 5x + 4}\\

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

a. (use a comma to separate answers as needed.)
b. the rational expression is defined for all real numbers.

Explanation:

Identify the condition for domain exclusion

Using the Domain Exclusion knowledge point

$$ x^2 + 5x + 4 = 0 $$

Factor the quadratic denominator

Using the Factoring Quadratic Trinomials knowledge point

$$ (x + 4)(x + 1) = 0 $$

Solve for the excluded values

Using the Zero-Product Principle knowledge point

$$
LATEXBLOCK0
$$

Answer:

• (A) \(-4, -1\) (Use a comma to separate answers as needed.) (Correct answer)
• (B) The rational expression is defined for all real numbers.