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Partial fractions split a single algebraic fraction into a sum of simpler fractions with linear or quadratic denominators, including repeated factors — an essential tool for integration, binomial expansion and differential equations. It appears across A-Level and iAL Pure Maths with the major exam boards. Learn it free on eClassroom through guided worked examples and instantly-marked exam-style questions.
How you do it
Factorise the denominator, then write one fraction for each factor with unknown numerators on top. Multiply through by the whole denominator and either substitute the roots to knock out terms or compare coefficients. A repeated factor needs a term for each power; a quadratic factor needs a linear numerator.
Before you start
The groundwork here is factorising and algebraic division. You will lean on this again for integration and binomial expansion of rational functions. You meet it in Pure 4.
What you learn
The course works through distinct linear factors, comparing coefficients, repeated factors, improper fractions and choosing the form and method. 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
Partial Fractions is part of the Algebra strand of our free A-level maths courses, studied in the AS year. It runs to 5 concepts, each followed by a check, with 5 worked examples along the way. Students often pair it with Quadratic Functions & Discriminant, Solving Quadratics and Transformations of Graphs. The Algebra revision engine gives you as many extra questions as you want, tracked on your skill tree.
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