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Simplifying Algebraic Fractions (WJEC GCSE Maths & Numeracy (Double Award)): Revision Note

Exam code: 3320

Naomi C

Written by: Naomi C

Reviewed by: Dan Finlay

Updated on

WJEC Maths & Numeracy (Double Award): HigherWJEC 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

Answer:

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 2 over denominator stretchy left parenthesis 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.