21
QuizMultiple Choice

Rational Functions — Test

Question 21 • Algebra II

What is the solution of the fraction with numerator x squared minus 1 and denominator x squared plus 5 x plus 4 is less than or equal to 0 ?

Answer
A
negative 4 is less than x comma x is less than or equal to 1 and x is not equal to negative 1
B
x is less than negative 4 or x is greater than or equal to 1
C
x is less than negative 4 or x is greater than negative 1
D
negative 4 is less than x comma x is less than 1 and x is not equal to negative 1

Explanation

Factor the numerator and denominator: (x² − 1)/(x² + 5x + 4) = (x − 1)(x + 1)/[(x + 1)(x + 4)]. The expression is undefined at x = −1 and x = −4, so both values must be excluded. After canceling the common factor, (x − 1)/(x + 4) is less than or equal to zero on −4 < x ≤ 1; excluding −1 gives the interval in choice B.

AI-written and checked against the verified answer.

Previous
Next