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.

[tex]\frac{x}{x^2-5x+6}+\frac{x}{x+3}\\\\Step 1: \frac{x}{(x-2)(x-3)}+\frac{x}{x+3}\\Step2: \frac{x}{(x-2)(x-3)}+\frac{x(x-2)}{(x-2)(x+3)}\\Step3:\frac{x(x+3)+x(x-2)(x+3)}{(x-2)(x-3)(x+3)}[/tex]

Lets consider the steps given in the question:

[tex]Step2: \frac{x}{(x-2)(x+3)}+\frac{3(x-2)}{(x-2)(x+3)}[/tex]

[tex]Step3: \frac{x+3(x-2)}{(x-2)(x+3)}\\[/tex]

Lets compare both solutions:

In the original solution, the denominator of first term is (x-2)(x-3)

In the solution given in the question, the denominator of first term is (x-2)(x+3).

So the mistake she did in step 2 was that she change the sign of 3 in (x-3) from negative to positive, due to which she gets the wrong common denominator shown in Step 3.

yoodyannapolis yoodyannapolis · Answer 2 · 2021-12-10T11:54:42+01:00

She used the wrong common denominator.

The given fraction is

[tex]\frac{x}{x^{2} -5x+6} +\frac{x}{x+3}\\\frac{x}{(x-3)(x+2)} +\frac{x}{x+3}\\\frac{x}{(x-3)(x+2) } +\frac{x(x+2)}{(x+2)(x+3)}\\[/tex]

And Riley answer is

Step 1: [tex]\frac{x}{(x-3)(x+2)} +\frac{3}{x+3}[/tex]

Step 2:[tex]\frac{x}{(x-2)(x+3)} +\frac{3(x-2)}{(x-2)(x+3}[/tex]

Step 3:[tex]\frac{x+3x-6}{(x-2)(x+3)}[/tex]

Step 4:[tex]\frac{4x-6}{(x-2)(x+3)}[/tex]

Here we see that Riley in step 2 Riley took the wrong denominator.

So, She used the wrong common denominator.

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