IGCSE Algebraic Fractions: Complete Guide for Cambridge IGCSE Mathematics

IGCSE algebraic fractions are essential algebra topics in Cambridge IGCSE Mathematics that appear in both Paper 2 and Paper 4. Mastering simplifying algebraic fractions, adding and subtracting, and multiplying and dividing is essential for solving complex algebraic problems.

This comprehensive IGCSE algebraic fractions guide covers everything you need to know, including simplifying, operations with algebraic fractions, worked examples, common exam questions, and expert tips from Tutopiya’s IGCSE maths tutors. We’ll also show you how to avoid the most common mistakes that cost students valuable marks.

🎯 What you’ll learn: By the end of this guide, you’ll know how to simplify algebraic fractions, add, subtract, multiply, and divide them, and apply these skills to solve problems in IGCSE exams.

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Why IGCSE Algebraic Fractions Matter

IGCSE algebraic fractions are essential algebra topics. Here’s why they’re so important:

• High frequency topic: Algebraic fraction questions appear regularly in IGCSE maths papers
• Foundation skill: Essential for advanced algebra and calculus
• Exam weight: Typically worth 4-8 marks per paper
• Real-world applications: Used in solving equations and simplifying expressions
• Problem-solving skills: Develops algebraic manipulation and fraction operations

Key insight from examiners: Students often struggle with finding common denominators or make errors when simplifying. This guide will help you master these systematically.

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Understanding Algebraic Fractions

Algebraic fractions are fractions where the numerator or denominator (or both) contain algebraic expressions.

Examples:

• (x + 2) / 3
• 5 / (x - 1)
• (x² - 4) / (x + 2)

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Simplifying Algebraic Fractions

Factorise numerator and denominator, then cancel common factors.

Example 1: Simplify (x² - 4) / (x + 2)

Solution: Factorise numerator: x² - 4 = (x + 2)(x - 2) (x² - 4) / (x + 2) = (x + 2)(x - 2) / (x + 2) = x - 2

Answer: x - 2

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Adding and Subtracting Algebraic Fractions

Find a common denominator, then add/subtract numerators.

Example 2: Simplify 3/(x + 1) + 2/(x - 1)

Solution: Common denominator: (x + 1)(x - 1) 3/(x + 1) + 2/(x - 1) = [3(x - 1) + 2(x + 1)] / [(x + 1)(x - 1)] = (3x - 3 + 2x + 2) / [(x + 1)(x - 1)] = (5x - 1) / [(x + 1)(x - 1)]

Answer: (5x - 1) / [(x + 1)(x - 1)]

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Multiplying Algebraic Fractions

Multiply numerators and denominators separately.

Example 3: Simplify (x + 2)/(x - 1) × (x - 3)/(x + 2)

Solution: (x + 2)/(x - 1) × (x - 3)/(x + 2) = (x + 2)(x - 3) / [(x - 1)(x + 2)] Cancel (x + 2): = (x - 3) / (x - 1)

Answer: (x - 3) / (x - 1)

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Dividing Algebraic Fractions

Multiply by the reciprocal.

Example 4: Simplify (x + 1)/(x - 2) ÷ (x + 3)/(x - 1)

Solution: (x + 1)/(x - 2) ÷ (x + 3)/(x - 1) = (x + 1)/(x - 2) × (x - 1)/(x + 3) = (x + 1)(x - 1) / [(x - 2)(x + 3)]

Answer: (x + 1)(x - 1) / [(x - 2)(x + 3)]

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Common Examiner Traps

• Forgetting common denominator - Always find common denominator for addition/subtraction
• Cancellation errors - Only cancel factors, not terms
• Sign errors - Watch positive/negative signs carefully

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Practice Questions

Question 1

Simplify (x² - 9) / (x + 3)

Solution: Factorise: (x + 3)(x - 3) / (x + 3) = x - 3

Answer: x - 3

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Tutopiya Advantage: Personalised IGCSE Algebraic Fractions Coaching

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Frequently Asked Questions About IGCSE Algebraic Fractions

What are algebraic fractions?

Algebraic fractions are fractions where the numerator or denominator contain algebraic expressions.

How do I simplify algebraic fractions?

Factorise numerator and denominator, then cancel common factors.

How do I add algebraic fractions?

Find a common denominator, then add the numerators.

How do I multiply algebraic fractions?

Multiply numerators and denominators separately, then simplify.

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Related IGCSE Maths Resources

Strengthen your IGCSE Mathematics preparation with these comprehensive guides:

• IGCSE Factorisation: Complete Guide - Master factorisation
• IGCSE Simplifying Algebraic Expressions: Complete Guide - Master simplification
• IGCSE Maths Revision Notes, Syllabus and Preparation Tips - Complete syllabus overview, topic breakdown, and revision strategies
• IGCSE Past Papers Guide - Access free IGCSE past papers and exam resources

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Next Steps: Master IGCSE Algebraic Fractions with Tutopiya

Ready to excel in IGCSE algebraic fractions? Our expert IGCSE maths tutors provide:

• Personalized 1-on-1 tutoring tailored to your learning pace
• Exam-focused practice with real Cambridge IGCSE past papers
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• Flexible scheduling to fit your revision timetable

Book a free IGCSE maths trial lesson and get personalized support to master algebraic fractions and achieve your target grade.

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