Algebraic Fractions summary

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

Difference of squares.

Worked example 2 — Multiply

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

Working

Cancel common factors.

Worked example 3 — Add

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

Working

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.