Simplifying Algebraic Fractions #1

The rules of fractions are no different for expressions that involve variables than they are for expressions involving only constants. Many students make errors when simplifying fractions, most often by “cancelling out” terms that are not factors of both the numerator and the denominator.

If you wish to simplify a fraction, you may only do so if the term to be cancelled is a factor of both the numerator and the denominator.

The answer shown below is wrong.  Try working your way through the problem backwards, from the answer up. As you find each mistake, try to identify the thinking behind it… what perspective led to the mistake? What should have been done instead?

\dfrac{2m+6}{2m}+\dfrac{3-9m}{3m}

= 6+\dfrac{3-9m}{3m}

=6+\dfrac{3(3m)}{3m}

=6+3

=9

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Hint 1: The correct answer to the problem in the first line above is

\dfrac{-2m+4}{m}

Hint 2: Two mistakes have been made in the work shown above.