Common Algebra Mistakes
Example: Simplifying an Expression

The Goal

Simplify the 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

If we look carefully at the mistake, we see that the expression has the form


which the student has mistakenly rewritten in the form


But only common factors of the numerator may be rewritten this way, for example, if the expression had the form


then it could be rewritten as follows:


A nice way to simplify the original expression is to multiply by 1 in the form shown in "The Correction", chosen so that the negative exponent factors in the numerator are cleared.

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