Common Algebra Mistakes
Example: Improper Cancellation

The Goal

Simplify the rational expression:


The Mistake

Find the algebra mistake:


(Roll the mouse over the algebra to see a hint in red)

The Correction


(Roll the mouse over the area above to see the correction in blue)

An Explanation

Any quantity to be canceled must be a common factor of the entire numerator and the entire denominator. There are no common factors, so this expression cannot be simplified.
(There are other mistakes: after incorrectly canceling the 8y and the 8x the student replaced these quantities with 0 instead of 1; even allowing for these errors, the sign of the final answer is wrong, too, perhaps the result of incorrectly multiplying the two minus signs in the denominator!)

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