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Fractions Review (page 5 of 5)

Sections: Reducing fractions, Mixed numbers and improper fractions, Multiplying and dividing fractions, Adding and subtracting fractions, Adding polynomial fractions

The procedure for adding numerical fractions works perfectly well on rational expressions, too:

  • Simplify (x + 2)/(x - 4) - (x + 1)/(x + 4)

    First, find the LCM:

      finding the LCM: (x - 4)(x + 4)

    Then convert and simplify:

      simplification: 3(3x + 4)/[(x - 4)(x + 4)]

As you can see from the above example, even if your calculator can do numerical fractions for you, you will still need to know the common-denominator algorithm (the "always-the-same process" for finding common denominators), because, when you get to rational expressions (polynomial fractions), your calculator won't likely be able to help you.

  • Simplify  x/(x^2 + 5x +6) - 2/(x^2 + 3x + 2)
    • finding the LCM: (x + 1)(x + 2)(x + 3)
          Copyright Elizabeth Stapel 2000-2011 All Rights Reserved

      simplification: (x - 3)/[(x + 1)(x + 3)]

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Cite this article as:

Stapel, Elizabeth. "Fractions Review." Purplemath. Available from Accessed


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