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Algebraic Fractions

Algebraic Fractions

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Lesson

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8 minute activity

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Worked example showing an algebraic fraction factorised from (x^2+6x)/(x^2+8x+12) to x(x+6)/((x+2)(x+6)) and then simplified to x/(x+2), with the common factor x+6 highlighted

An algebraic fraction is a fraction whose numerator, denominator, or both contain algebra. The top is called the numerator and the bottom is called the denominator.

They follow the same rules as ordinary fractions, but you can only cancel common factors. You must not cancel part of a sum such as the xxx in x+4x+4x+4.

That is why factorising comes first. Useful patterns are:

3x2+9x=3x(x+3) 3x^2+9x = 3x(x+3) 3x2+9x=3x(x+3) x2+7x+10=(x+5)(x+2) x^2+7x+10 = (x+5)(x+2) x2+7x+10=(x+5)(x+2) x2−25=(x−5)(x+5) x^2-25 = (x-5)(x+5) x2−25=(x−5)(x+5)

Questions

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64 exam-style questions

Practice questions

Question 1

2 marks

Simplify fully x2+5xx2+7x+10\displaystyle \frac{x^2 + 5x}{x^2 + 7x + 10}x2+7x+10x2+5x​

Flashcards

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23 flashcards

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What specific part of an algebraic fraction is the only part allowed to be cancelled?

Algebraic Fractions Revision Guide

  1. GCSE
  2. /Maths
  3. /Algebraic Fractions

Revision notes for CCEA GCSE Maths Algebraic Fractions: explanations and worked examples.

Practise questions

1 of 5

Simplify fully x2+5xx2+7x+10\frac{x^2+5x}{x^2+7x+10}x2+7x+10x2+5x​.