AnswersAlgebra IIRational Functions — TestQuestion 21
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Rational Functions — Test

Question 21 • Algebra II

Mr. Knotts found the difference of the following expression. Which statement is true about Mr. Knotts’s work? the fraction with numerator x and denominator x squared minus 1 minus the fraction with numerator 1 and denominator x minus 1 Knotts’s Work Step 1: the fraction with numerator x and denominator open paren x plus 1 close paren times open paren x minus 1 close paren minus the fraction with numerator 1 and denominator x minus 1 Step 2: the fraction with numerator x and denominator open paren x plus 1 close paren times open paren x minus 1 close paren minus the fraction with numerator 1 times open paren x plus 1 close paren and denominator open paren x plus 1 close paren times open paren x minus 1 close paren Step 3: the fraction with numerator x minus x plus 1 and denominator open paren x plus 1 close paren times open paren x minus 1 close paren Step 4: the fraction with numerator 1 and denominator open paren x plus 1 close paren times open paren x minus 1 close paren

Answer
A
In step 4, he did not correctly subtract the numerator.
B
In step 2, he did not use the correct common denominator.
C
In step 3, he did not distribute the negative sign when he subtracted.
D
In step 1, he did not correctly factor the denominator.

Explanation

Step 1 correctly factors x² − 1 as (x + 1)(x − 1), and step 2 gives both fractions the common denominator (x + 1)(x − 1). When subtracting the numerators, however, x − (x + 1) should become x − x − 1 because the negative sign applies to both terms in the parentheses. Mr. Knotts wrote x − x + 1 in step 3, so he did not distribute the negative sign correctly.

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