Rational Expressions (CIE A Level Maths: Pure 3)

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