Topic summary · Pure advanced (P3)

Algebraic Fractions summary

Algebraic fractions simplify by factorising and cancelling common factors, then combine over a common denominator.

Open Learning Sheet — Algebraic Fractions Download Algebraic Fractions answers PDF

Files: P3-Algebraic Fractions.pdf · P3-Algebraic Fractions answers.pdf · free public downloads · diagrams in the PDFs

Key learning points

Factorise fully before cancelling; state excluded values.
Add/subtract using a common denominator from factor products.
If improper, divide polynomials first.
Partial fractions start from proper rational functions.

Worked example 1 — Simplify

Simplify $\tfrac{x^2-9}{x+3}$ .

Working

x-3\ (x\ne-3)

Difference of squares.

Worked example 2 — Multiply

Simplify $\tfrac{2}{x}\times\tfrac{x^3}{4}$ .

Working

\tfrac{x^2}{2}

Cancel common factors.

Worked example 3 — Add

Simplify $\tfrac{1}{x}+\tfrac{2}{x+1}$ .

Working

\tfrac{3x+1}{x(x+1)}

Common denominator.

Scaffolded Learning Sheet and answers (PDFs)

This page is a short, searchable overview for revision and search engines. Use the Scaffolded Learning Sheet first, then the Answers PDF for a full written solution. The printable PDFs remain the main classroom resource.

Open Learning Sheet Answers PDF

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