IGCSE Math RevisionQuestion 1
Simplify \(\frac{6x^2}{9x}\).
Show the worked answer
- Divide top and bottom by \(3x\).
Answer: \(\frac{2x}{3}\)
Cambridge IGCSE Maths (0580) · Topic 2: Algebra and graphs · 2.3
Cambridge IGCSE Maths 0580 Algebraic Fractions Questions
Algebraic Fractions questions with worked answers for Cambridge IGCSE Mathematics (0580). Each question says whether it is Core or Extended and whether it is for a calculator or non-calculator paper. Try each one before you open the answer.
- 8 questions
- 8 Extended
- 8 non-calculator
- Free, no sign-in
What the syllabus asks
- 2.3 Algebraic fractions Extended only
Extended: Add, subtract, multiply and divide algebraic fractions; Factorise and simplify rational expressions.
Summarised in our own words: check the exact wording in the official 0580 syllabus.
Algebraic Fractions questions: Extended
Extended content, for Papers 2 and 4.
Question 2
Write \(\frac{x}{3} + \frac{x}{4}\) as a single fraction.
Show the worked answer
- Common denominator \(12\): \(\frac{4x}{12} + \frac{3x}{12}\).
Answer: \(\frac{7x}{12}\)
Question 3
Simplify \(\frac{x^2 - 9}{x^2 + 3x}\).
Show the worked answer
- Top: \((x + 3)(x - 3)\). Bottom: \(x(x + 3)\).
- Cancel the common factor \((x + 3)\).
Answer: \(\frac{x - 3}{x}\)
Question 4
Simplify \(\frac{x^2 + 5x + 6}{x^2 - 4}\).
Show the worked answer
- Top: \((x + 2)(x + 3)\). Bottom: \((x + 2)(x - 2)\).
- Cancel \((x + 2)\).
Answer: \(\frac{x + 3}{x - 2}\)
Question 5
Write \(\frac{2}{x + 1} + \frac{3}{x - 2}\) as a single fraction in its simplest form.
Show the worked answer
- Common denominator \((x + 1)(x - 2)\).
- Top: \(2(x - 2) + 3(x + 1) = 2x - 4 + 3x + 3 = 5x - 1\).
Answer: \(\frac{5x - 1}{(x + 1)(x - 2)}\)
Question 6
Write \(\frac{3x}{x - 4} - 2\) as a single fraction.
Show the worked answer
- \(2 = \frac{2(x - 4)}{x - 4}\)
- \(\frac{3x - 2x + 8}{x - 4} = \frac{x + 8}{x - 4}\)
Answer: \(\frac{x + 8}{x - 4}\)
Question 7
Simplify \(\frac{x^2 - x}{4x + 8} \times \frac{x + 2}{x^2 - 1}\).
Show the worked answer
- Factorise: \(\frac{x(x - 1)}{4(x + 2)} \times \frac{x + 2}{(x - 1)(x + 1)}\).
- Cancel \((x - 1)\) and \((x + 2)\).
Answer: \(\frac{x}{4(x + 1)}\)
Question 8
Solve \(\frac{6}{x} - \frac{6}{x + 1} = 1\).
Show the worked answer
- Multiply every term by \(x(x + 1)\): \(6(x + 1) - 6x = x(x + 1)\).
- \(6 = x^2 + x\), so \(x^2 + x - 6 = 0\).
- \((x + 3)(x - 2) = 0\)
Answer: \(x = 2\) or \(x = -3\)
Every question on this page is original, written for IGCSE Math Revision rather than taken from Cambridge papers, and each answer was re-solved independently before publishing. Questions with a mark scheme come from our 0580 practice bank (M method, A accuracy, B independent marks).
Keep going
- Algebra and graphs practice for 0580: more questions, each one marked, tagged Core or Extended
- My mistakes, then a Skill Builder on the skills you missed
- Common mistakes in 0580: what the Cambridge examiner reports say
- Algebra and graphs revision notes and the 0580 formula sheet
- Cambridge IGCSE Maths 0580 past papers, when you are ready for a full paper
Questions students ask
Which Cambridge 0580 papers can test algebraic fractions?
Algebraic Fractions is Extended content (syllabus 2.3), so it is tested only on the Extended papers, Paper 2 (non-calculator) and Paper 4 (calculator). Core candidates do not need it.
Are these Cambridge past-paper questions?
No. Every question here was written for IGCSE Math Revision in the style of the 0580 papers, and each answer was checked independently before publishing. For real exam practice, use the Cambridge past papers linked from our 0580 past papers page.
Where can I practise more algebraic fractions questions?
In the 0580 practice for topic 2 (Algebra and graphs), where every question is marked and tagged Core or Extended. Practice is part of the IGCSE plan, with a free preview; the questions on this page are free.