Question

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

x/x^2-5x+6 + 3/x+3


Step 1: x/(x-2)(x-3) + 3/x+3


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


Step 3: x+3x-6/(x-2)(x+3)


Step 4: 4x-6/(x-2)(x+3)



A. She added the two fractions incorrectly.


B. She used the wrong common denominator.


C. She did not distribute the negative correctly.


D. She did not multiply the first fraction by a factor.

Answer 1

B

Explanation:

Just did it

Answer 2

We have been given work of Riley. By looking at his work carefully, we have to identify the error. So let's start from beginning.

`(x)/(x^2-5x+6)+ (3)/(x+3)`

First line is just the question so there will be no error.

After that we try to factor denominators

STEP1:
`(x)/((x-2)(x-3))+ (3)/(x+3)`

Factors are correct so no error in step1.

In step2, we have to find the common denominator which will be (x-2)(x-3)(x+3)

so that means she needs to multiply and divide 2nd term by (x-2)(x-3) while she multiplied by only (x-2). Which means she used wrong common denominator.

Hence final answer will be "B. She used the wrong common denominator."