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Simplifying Algebraic Fractions (Cambridge (CIE) IGCSE Maths)

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Mark Curtis

Written by: Mark Curtis

Reviewed by: Dan Finlay

Cambridge (CIE) Maths: ExtendedEdexcel Maths A (Modular): Higher Unit 1Cambridge (CIE) International Maths: ExtendedEdexcel Maths A: Higher

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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
    Mark Curtis

    Author: Mark Curtis

    Expertise: Maths

    Mark graduated twice from the University of Oxford: once in 2009 with a First in Mathematics, then again in 2013 with a PhD (DPhil) in Mathematics. He has had nine successful years as a secondary school teacher, specialising in A-Level Further Maths and running extension classes for Oxbridge Maths applicants. Alongside his teaching, he has written five internal textbooks, introduced new spiralling school curriculums and trained other Maths teachers through outreach programmes.

    Dan Finlay

    Author: Dan Finlay

    Expertise: Maths 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.