Algebraic Fractions
GCSE and IGCSE algebra support for simplifying and solving fractions.
Applying fraction rules to algebraic expressions
An algebraic fraction contains an algebraic expression in its numerator, denominator or both. GCSE Higher and IGCSE students use ordinary fraction rules together with factorisation and equation solving. Values that make a denominator zero must be excluded.
Key knowledge and method
Factorise fully before cancelling, because only common factors may be cancelled. To add or subtract, create a common denominator. To divide, multiply by the reciprocal. When solving an equation, multiply every term by the lowest common denominator. Review factorisation and expanding brackets
Worked examples
Example 1: Simplify 6x² ÷ 9x. Cancel common factors to obtain 2x/3, where x ≠ 0. Example 2: Simplify (x² - 9)/(x + 3). Factorise the numerator as (x - 3)(x + 3), giving x - 3, where x ≠ -3. Example 3: Add 2/x + 3/(2x). The common denominator is 2x, so 4/(2x) + 3/(2x) = 7/(2x).
Common mistakes and exam advice
Do not cancel terms joined by addition or subtraction. For example, x cannot be cancelled from (x + 2)/x. Factor first, state excluded values where required and multiply every term when clearing denominators. The glossary entry for an expression helps distinguish terms and factors.
Practice exercises and answers
Exercise 1: Simplify 8x/12. Answer: 2x/3. Exercise 2: Simplify (x² - 16)/(x + 4). Answer: x - 4, where x ≠ -4. Exercise 3: Add 1/x + 2/(3x). Answer: 3/(3x) + 2/(3x) = 5/(3x), where x ≠ 0.
Related learning across the website
Build the necessary skills through Fractions Lessons, Algebra Lessons, GCSE algebra help, quadratic equation lessons, linear equations, quadratic equations glossary, equations, variables, coefficients and rearranging formulae
Benefits of one-to-one maths tutoring
One-to-one lessons with maths tutor Ryan Harvey can diagnose whether difficulty comes from ordinary fractions, factorisation or algebraic notation and provide targeted practice.
Contact and lesson enquiry
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