Algebraic Fractions for IGCSE Maths
Simplifying, adding, subtracting, multiplying, and dividing algebraic fractions. This subtopic is part of Algebra in the Cambridge IGCSE Mathematics 0580 syllabus (Extended tier only). Understanding a
What You Need to Know
Simplifying, adding, subtracting, multiplying, and dividing algebraic fractions. This subtopic is part of Algebra in the Cambridge IGCSE Mathematics 0580 syllabus (Extended tier only). Understanding algebraic fractions is essential for achieving a strong grade in your IGCSE Maths exam.
Understanding Algebraic Fractions
Algebraic fractions behave exactly like numerical fractions but with expressions in the numerator and denominator. Key skills for IGCSE Extended: simplifying (factorise and cancel common factors), adding/subtracting (find common denominator), multiplying (multiply numerators and denominators), dividing (multiply by the reciprocal), and solving equations containing algebraic fractions (multiply through by the LCM to clear denominators).
Step-by-Step Method
- 1
Simplify: factorise numerator and denominator
Factorise both parts fully, then cancel any common factors. E.g. (x²−4)/(x+2) = (x+2)(x−2)/(x+2) = x−2.
- 2
Add/subtract: find the common denominator
Identify the LCM of the denominators. Rewrite each fraction with the common denominator, then add/subtract numerators.
- 3
Multiply: multiply straight across
Multiply numerators together and denominators together. Simplify by cancelling before multiplying where possible.
- 4
Divide: multiply by the reciprocal
Flip the second fraction and multiply. Always simplify before multiplying.
- 5
Solve equations: clear denominators
Multiply every term by the LCM of all denominators. This eliminates all fractions, leaving a standard equation to solve.
Worked Example
Question
Simplify: (x² + 5x + 6)/(x² − x − 6).
Solution
Step 1: Factorise numerator. x² + 5x + 6 = (x+2)(x+3) Step 2: Factorise denominator. x² − x − 6 = (x+2)(x−3) Step 3: Cancel common factor. (x+2)(x+3) / (x+2)(x−3) = (x+3)/(x−3) Answer: (x+3)/(x−3)
Exam Tips for Algebraic Fractions
- Always factorise before cancelling — never cancel terms that are added (e.g. (x+3)/(x+5) ≠ 3/5).
- When adding fractions, the denominator stays as the LCM — only add the numerators.
- For solving equations, multiply every term (including integer terms) by the LCM — a common error is missing one term.
- State restrictions: when cancelling (x+2), note x ≠ −2. Examiners rarely penalise for missing this but it shows understanding.
Practice Questions
Q1: Simplify: (2x² − 8)/(x² − x − 6).
Show hint
Factor numerator: 2(x+2)(x−2). Factor denominator: (x−3)(x+2). Cancel (x+2).
Q2: Write as a single fraction: 3/(x+1) + 2/(x−2).
Show hint
Common denominator = (x+1)(x−2). Rewrite each fraction, then add numerators.
Q3: Solve: 3/(x−1) − 1/(x+2) = 0.
Show hint
Multiply through by (x−1)(x+2): 3(x+2) − (x−1) = 0. Expand and solve.
Frequently Asked Questions
What is algebraic fractions in IGCSE Maths?
Simplifying, adding, subtracting, multiplying, and dividing algebraic fractions.
Is algebraic fractions in the Core or Extended syllabus?
Algebraic Fractions is part of the Extended only syllabus for IGCSE Mathematics 0580.
How do I revise algebraic fractions effectively?
Start with the revision notes to understand key concepts, then work through the worked examples step by step. Finally, practise past paper questions under timed conditions. Teacher Rig recommends spending focused revision sessions on algebraic fractions rather than trying to cover everything at once.
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