Question

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. Mark this and return

Answer 1

The mathematical mistake that Riley made is that: "She used the wrong common denominator." (Option A)

What is a Common Denominator?

A common denominator is a factor that is similar to all the fractions in the sequence of equations.

Hence the correct answer is:

(2(2x² - 6x + 9))/((x-3) (x-2) (x+3))

See the correct sequence of steps below:

Step One - the Expression is given as:

(x/(x-3)(x-2)) + (3/(x+3))

Step 2 - Find the common denominator and rewrite the expression so that the numerators are above the common denominators.

Hence we have:  (x (x+3) + 3(x-3) (x-2))/(x-3)(x-2)(x+3)

Step 3  Apply the Law of Multiplicative Distribution:

Hence we have  (x² +3x+3x²-9x-6x+16)/(x-3)(x-2)(x+3)

Step 4 -  Collect Like Items

This gives us: (x²+3x²)+(3x-9x-6x)+18/(x-3)(x-2)(x+3)

Step 5 Sort for like coefficients

This gives us:  ((1+3)x² +(3-9-6) * x + 18)/(x-3)(x-2)(x+3)

Step 6 -  check for the sum or difference

This gives us: (4x²+(3-9-6) * x+ 18)/(x-3)(x-2)(x+3)

We simplify and factor the expression to get

(2(2x²-6x+6)/(x-3)(x-2)(x+3).

Learn more about Common Denominators at:

brainly.com/question/542317

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