GCSEMathsWJEC EduqasHigherRevision Notes2. AlgebraAlgebraic FractionsSimplifying Algebraic Fractions

Simplifying Algebraic Fractions (WJEC Eduqas GCSE Maths): Revision Note

Exam code: C300

Naomi C

Written by: Naomi C

Reviewed by: Dan Finlay

Updated on

WJEC Eduqas Maths: HigherOCR Maths: HigherAQA Maths: HigherEdexcel Maths: Higher

Simplifying algebraic fractions

What is an algebraic fraction?

  • An algebraic fraction is a fraction with an algebraic expression on the top (numerator) and/or the bottom (denominator)

How do you simplify an algebraic fraction?

  • If possible, factorise fully the top and bottom

    • E.g. fraction numerator 2 x over denominator x squared plus 3 x end fraction equals fraction numerator 2 x over denominator x open parentheses x plus 3 close parentheses end fraction

  • Cancel common factors

    • This factor may be a single term

      • E.g. fraction numerator up diagonal strike x open parentheses 5 x minus 1 close parentheses over denominator 4 up diagonal strike x end fraction equals fraction numerator 5 x minus 1 over denominator 4 end fraction

    • It could also be a common bracket

      • E.g. fraction numerator x up diagonal strike open parentheses x plus 2 close parentheses end strike over denominator up diagonal strike open parentheses x plus 2 close parentheses end strike open parentheses x minus 1 close parentheses end fraction equals fraction numerator x over denominator x minus 1 end fraction

  • A common mistake is to cancel a factor that is not common to all terms in either the top or the bottom of a fraction

    • E.g. The fraction fraction numerator 6 x over denominator x plus 1 end fraction cannot be simplified

      • x is not common to all terms in the bottom of the fraction

      • and the expression on the bottom cannot be factorised

Examiner Tips and Tricks

  • When asked to simplify an algebraic fraction, factorise top and bottom

    • It is very likely that one of the factors will be the same on the top and the bottom

    • Use this fact to help you, if one of the expressions is difficult to factorise!

Worked Example

Simplify fraction numerator 4 x plus 6 over denominator 2 x squared minus 7 x minus 15 end fraction

Factorise the top, by using 2 as a common factor

fraction numerator 2 open parentheses 2 x plus 3 close parentheses over denominator 2 x squared minus 7 x minus 15 end fraction

Factorise the bottom using your preferred method
Using the fact that the top factorised to open parentheses 2 x plus 3 close parentheses may help!

fraction numerator 2 open parentheses 2 x plus 3 close parentheses over denominator open parentheses 2 x plus 3 close parentheses open parentheses x minus 5 close parentheses end fraction

The common factors on the top and bottom reduce to 1 (cancel out)

fraction numerator 2 up diagonal strike open parentheses 2 x plus 3 close parentheses end strike over denominator up diagonal strike open parentheses 2 x plus 3 close parentheses end strike open parentheses x minus 5 close parentheses end fraction

fraction numerator bold 2 over denominator stretchy left parenthesis bold italic x minus 5 stretchy right parenthesis end fraction

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    Author
    Reviewer
    Naomi C

    Author: Naomi C

    Expertise: Maths Content Creator

    Naomi graduated from Durham University in 2007 with a Masters degree in Civil Engineering. She has taught Mathematics in the UK, Malaysia and Switzerland covering GCSE, IGCSE, A-Level and IB. She particularly enjoys applying Mathematics to real life and endeavours to bring creativity to the content she creates.

    Dan Finlay

    Reviewer: Dan Finlay

    Expertise: Maths Subject Lead

    Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.