Common Algebra Mistakes
Example: Simplify an Expression

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

Care is needed when multiplying out expressions. The parentheses indicate that both x2 and 1 must be multiplied by 2. The two 2s must be multiplied together in the term 2x(2x). Slow down and check your work!
(Tempted to cancel the (x2 + 1) in the numerator and one of the (x2 + 1) factors in the denominator? You cannot! To cancel a factor it needs to be a common factor of the entire numerator and the entire denominator. In this case (x2 + 1) is not a common factor of the entire numerator)

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