Rational Expressions (Cambridge (CIE) A Level Maths: Pure 3): Revision Note

Rational expressions

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)

 How do I simplify rational expressions?

• You may need to recall the factor theorem

• Start by factorising polynomials using factor theorem or algebraic division

Simplify $\frac{x^3-7x+6}{x^2+2x-3}$

• cancel any common (linear) factors

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