Question

1. ) Explain the error in this simplification
2.) Show your work as you correct the error

Answer 1

Answer:

Given equation:

• 1 - 2/(x - 2) = (x + 1)/(x + 2)

Correct solution:

• (x - 2 - 2)/(x - 2) = (x + 1)/(x + 2)         complete the fraction on the left
• (x - 4)(x + 2) = (x + 1)(x - 2)                 cross-multiply
• x² + 2x - 4x - 8 = x² - 2x + x - 2         open parenthesis
• -2x - 8 = -x - 2                                    simplify
• -x = 6
• x = -6

Errors

• Step 1.  not counting 1 as part of equation. It wasn't included into fraction.
• Step 1.  not multiplying (x - 2) by 1.
• Step 4. - x + 2x = -2x is incorrect, it should be x