Asked by htht

Riley makes a mistake in step 2 while doing her homework. What was her mistake?

StartFraction x Over x squared minus 5 x + 6 EndFraction + StartFraction x Over x + 3 EndFraction

Step 1: StartFraction x Over (x minus 2)(x minus 3) EndFraction + StartFraction 3 Over x + 3 EndFraction

Step 2: StartFraction x Over (x minus 2) (x + 3) EndFraction + 3 (x minus 2) Over (x minus 2) (x + 3) EndFraction

Step 3: StartFraction x + 3 x minus 6 Over (x minus 2) (x + 3) EndFraction

Step 4: StartFraction 4 x minus 6 Over (x minus 2) (x + 3) EndFraction
She added the two fractions incorrectly.
She used the wrong common denominator.
She did not distribute the negative correctly.
She did not multiply the first fraction by a factor.

All Answers 1

Answered by GPT-5 mini AI
She used the wrong common denominator.

In step 2 Riley changes the denominators to (x−2)(x+3) but the original denominators are (x−2)(x−3) and (x+3). The correct common denominator is (x−2)(x−3)(x+3), so she should have multiplied the first fraction by (x+3)/(x+3) and the second by (x−2)(x−3)/(x−2)(x−3).