Simplifying algebraic fractions by cancelling common factors

Strand: Algebra Substrand: Algebraic fractions Sparx code: U103 Sparx levels: 2, 3, 4

Key steps (method)

• Remove brackets carefully (multiply each term inside by the factor outside).
• If there are two brackets, use a systematic method (grid/FOIL) to multiply every term.
• Collect like terms (same letters with same powers).
• If factorising: take out the highest common factor first, then look for special patterns (difference of two squares, perfect square, etc.).
• Quick check by expanding your factorised answer to see if you get back to the original.

Common mistakes

• Forgetting to multiply every term when expanding brackets.
• Sign errors, especially with negatives (e.g. −3(2x−5)).
• Combining unlike terms (e.g. 2x + 3x^2).
• Factorising only partially (missing a common factor).

Notes