Rational Expressions (Cambridge (CIE) A Level Maths): Revision Note

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)

Factor theorem

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

 How to simplify a rational expression (algebraic fraction)

• Start by factorising polynomials using factor theorem or algebraic division

Simplify 

• cancel any common (linear) factors

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