Algebraic Fractions Topic Review summary

Key learning points

• Factor numerators and denominators before cancelling.
• Multiply numerators/denominators; divide by multiplying by the reciprocal.
• Add/subtract via a common denominator from factorised denominators.
• Clear denominators to solve equations (state exclusions).
• Track values that make any denominator zero.

Worked example 1 — Simplify

$\frac{x^2-1}{x^2+x}$.

Working

Factor then cancel.

Worked example 2 — Add

$\frac{1}{x}+\frac{1}{x+1}$.

Working

Common denominator.

Worked example 3 — Factor numerators and denominators before

Apply this idea from the Topic Review: Factor numerators and denominators before cancelling.

Working

Attempt without notes, then check the answers PDF.

Worked example 4 — Multiply numerators/denominators; divide b

Apply this idea from the Topic Review: Multiply numerators/denominators; divide by multiplying by the reciprocal.

Working

Attempt without notes, then check the answers PDF.

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.