Question

These are the steps Brittany took to find the difference, but she made a mistake. Select the step at which Brittany made her first mistake. Then select the correct difference in simplest form. Select all the correct locations on the image.

Answer 1

Explanation:

Answer 2

Brittany's first mistake is in step 3. She incorrectly simplifies the expression
`$(4(x-4))/((x-4)(x+3))$` to
`$(4)/(x+3)$`. The correct simplification is
`$(4)/(x-4)$`.

Brittany's first mistake is in Step 3. She incorrectly simplifies the expression
`$(4(x-4))/((x-4)(x+3))$` to
`$(4)/(x+3)$`. The correct simplification is
`$(4)/(x-4)$`.

Here is a step-by-step explanation of Brittany's error:

Step 2:

=
`(x^(2)-29)/((x+3)(x-2))-(4(x-4))/((x-4)(x+3))`

Step 3:

=
`(x^(2)-29)/((x+3)(x-2))-(4)/(x+3)`

Brittany's mistake: In this step, Brittany cancels the x-4 factor from the numerator and denominator of the second term. This is incorrect because the x-4 factor is not present in the denominator of the first term.

Correct simplification:

=
`(x^(2)-29)/((x+3)(x-2))-\frac{4\cancel{(x-4})}{\cancel{(x-4)}(x+3)}`

=
`(x^(2)-29)/((x+3)(x-2))-(4)/(x+3)`

If Brittany had correctly simplified the expression in Step 3, her subsequent steps would have been correct. The correct difference in simplest form is therefore:

=
`(x^(2)-4x-37)/((x+3)(x-2))`

Answers:

Step at which Brittany made her first mistake: Step 3

Correct difference in simplest form:
`$(x^(2)-4x-37)/((x+3)(x-2))$`