The Goal

Find

The Mistake

Find the mistake:

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The Correction

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An Explanation

The technique of factoring the numerator and then cancelling (which is valid since x is never actually equal to three in the limit computation) is an appropriate strategy. The first mistake was to factor incorrectly. The second mistake was one of haste; it appears that the cancellation was done in the student's head and then 0, instead of 3, was substituted for x to arrive at an answer.