IGCSEMathsEdexcelMaths A (Modular)Higher Unit 1Revision NotesAlgebraAlgebraic FractionsSimplifying Algebraic Fractions

Simplifying Algebraic Fractions (Edexcel IGCSE Maths A (Modular))

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Mark Curtis

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Maths

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. $\frac{2 x}{x^{2} + 3 x} = \frac{2 x}{x (x + 3)}$
Cancel common factors
- This factor may be a single term
  - E.g. $\frac{x (5 x - 1)}{4 x} = \frac{5 x - 1}{4}$
- It could also be a common bracket
  - E.g. $\frac{x (x + 2)}{(x + 2) (x - 1)} = \frac{x}{x - 1}$
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 $\frac{6 x}{x + 1}$ 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

Exam Tip

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 $\frac{4 x + 6}{2 x^{2} - 7 x - 15}$

Factorise the top, by using 2 as a common factor

$\frac{2 (2 x + 3)}{2 x^{2} - 7 x - 15}$

Factorise the bottom using your preferred method
Using the fact that the top factorised to $(2 x + 3)$ may help!

$\frac{2 (2 x + 3)}{(2 x + 3) (x - 5)}$

The common factors on the top and bottom reduce to 1 (cancel out)

$\frac{2 (2 x + 3)}{(2 x + 3) (x - 5)}$

$\frac{2}{(x - 5)}$

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Author: Mark Curtis

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.