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A LevelMaths: PureAQARevision Notes2. Algebra & Functions2.6 Rational Expressions2.6.1 Rational Expressions

Rational Expressions (AQA A Level Maths: Pure): Revision Note

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Rational Expressions (Algebraic Fractions)

What are rational expressions?

  • Rational numbers are numbers that can be written as a fraction (quotient)

    Rational comes from ratio – a number is rational if it can be written as a ratio of two integers – ie a fraction!

  • A rational expression is an algebraic fraction

    The ratio between two algebraic expressions (usually polynomials)

 

Rational Expressions Notes Diagram 1, A Level & AS Level Pure Maths Revision Notes

Factor theorem

  • In order to simplify a rational expression you'll need to remember the factor theorem

Rational Expressions Notes Diagram 2, A Level & AS Level Pure Maths Revision Notes

 

How to simplify a rational expression (algebraic fraction)Rational Expressions Notes Diagram 5, A Level & AS Level Pure Maths Revision Notes

  • Start by factorising polynomials using factor theorem or algebraic division

Simplify fraction numerator x cubed minus 7 x plus 6 over denominator x squared plus 2 x minus 3 end fraction

Rational Expressions Notes Diagram 3, A Level & AS Level Pure Maths Revision Notes  

  • cancel any common (linear) factors

 Rational Expressions Notes Diagram 4, A Level & AS Level Pure Maths Revision Notes  

  • recognise a top-heavy (improper) rational expression, simplify if needed

Worked example

Rational Expressions Example Diagram, A Level & AS Level Pure Maths Revision Notes

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    Paul

    Author: Paul

    Expertise: Maths

    Paul has taught mathematics for 20 years and has been an examiner for Edexcel for over a decade. GCSE, A level, pure, mechanics, statistics, discrete – if it’s in a Maths exam, Paul will know about it. Paul is a passionate fan of clear and colourful notes with fascinating diagrams – one of the many reasons he is excited to be a member of the SME team.