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Algebraic fractions have polynomials in the numerator and denominator. This topic covers simplifying them by factorising and cancelling, and adding, subtracting, multiplying and dividing them. It's a key topic in A-Level and International A-Level (iAL) Pure Mathematics. This free interactive course teaches the method with worked examples and gives instant-feedback practice questions to lock it in.
How you do it
Factorise every numerator and denominator first, then cancel common factors — never individual terms across a sum. For addition, find a common denominator. For division, flip and multiply.
Before you start
Start once you are confident with factorising and fraction arithmetic. You will lean on this again for improper fractions and partial fractions.
What you learn
Fractions with algebra in them obey exactly the same rules as ordinary fractions — you just have to factorise first. To simplify an algebraic fraction, factorise the top and the bottom, then cancel anything common. Exactly as with numbers — but factorise everything first, so you can cancel before you multiply. The course works through simplifying: factorise, then cancel, multiplying and dividing, adding and subtracting, fractions within fractions, harder simplification and equations with algebraic fractions. Every section has instant-feedback practice questions matched to Edexcel International A-Level and 9MA0 Pure, and the course finishes with full exam-style questions you mark yourself.
Related Topics
Algebraic Fractions is a Algebra topic in the A-level syllabus, covered here at the AS year. You work through 6 concepts and 6 worked examples, testing yourself at 6 points. Students often pair it with Completing the Square, Composite and Inverse Functions, Factor & Remainder Theorem, Functions - Domain and Range and Improper Algebraic Fractions. For unlimited practice, the Algebra revision engine builds new questions on demand and records your accuracy.
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