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.

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).

See the attached for full question.

Learn more about Common Denominators at:

https://brainly.com/question/542317