Riley makes a mistake in step 2 while doing her homework. What was her mistake? the fraction with numerator x and denominator x squared minus 5 x plus 6 plus the fraction with numerator 3 and denominator x plus 3 Riley's Work Step 1: the fraction with numerator x and denominator open paren x minus 2 close paren times open paren x minus 3 close paren plus the fraction with numerator 3 and denominator x plus 3 Step 2: the fraction with numerator x and denominator open paren x minus 2 close paren times open paren x plus 3 close paren plus the fraction with numerator 3 times open paren x minus 2 close paren and denominator open paren x minus 2 close paren times open paren x plus 3 close paren Step 3: the fraction with numerator x plus 3 x minus 6 and denominator open paren x minus 2 close paren times open paren x plus 3 close paren Step 4: the fraction with numerator 4 x minus 6 and denominator open paren x minus 2 close paren times open paren x plus 3 close paren
Answer
A
She did not multiply the first fraction by a factor.
B
She added the two fractions incorrectly.
C
She did not distribute the negative correctly.
D
She used the wrong common denominator.
Explanation
The factored denominator in the first fraction is (x − 2)(x − 3), so a common denominator with the second fraction must include all three factors: (x − 2)(x − 3)(x + 3). In step 2, Riley uses (x − 2)(x + 3), leaving out (x − 3). Her mistake was using the wrong common denominator.
AI-written and checked against the verified answer.

Question

Riley makes a mistake in step 2 while doing her homework. What was her mistake? the fraction with numerator x and denominator x squared minus 5 x plus 6 plus the fraction with numerator 3 and denominator x plus 3 Riley's Work Step 1: the fraction with numerator x and denominator open paren x minus 2 close paren times open paren x minus 3 close paren plus the fraction with numerator 3 and denominator x plus 3 Step 2: the fraction with numerator x and denominator open paren x minus 2 close paren times open paren x plus 3 close paren plus the fraction with numerator 3 times open paren x minus 2 close paren and denominator open paren x minus 2 close paren times open paren x plus 3 close paren Step 3: the fraction with numerator x plus 3 x minus 6 and denominator open paren x minus 2 close paren times open paren x plus 3 close paren Step 4: the fraction with numerator 4 x minus 6 and denominator open paren x minus 2 close paren times open paren x plus 3 close paren

Answer

A

She did not multiply the first fraction by a factor.

B

She added the two fractions incorrectly.

C

She did not distribute the negative correctly.

D

She used the wrong common denominator.

Explanation

The factored denominator in the first fraction is (x − 2)(x − 3), so a common denominator with the second fraction must include all three factors: (x − 2)(x − 3)(x + 3). In step 2, Riley uses (x − 2)(x + 3), leaving out (x − 3). Her mistake was using the wrong common denominator.

AI-written and checked against the verified answer.

Revolt · Accepted Answer

She used the wrong common denominator.

Practice Test

Explanation

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