The idea

Simplifying, multiplying and dividing algebraic fractions

Why only FACTORS cancel — never terms — so factorising must come first, and how × and ÷ work exactly as for number fractions once everything is in factors.

A full journey — read it, play with it, work it, then earn real exam marks. Everything stays on the timeline below.

In this lesson — start anywhere

Algebra · Algebraic fractions

Simplifying, multiplying and dividing algebraic fractions

Why only FACTORS cancel — never terms — so factorising must come first, and how × and ÷ work exactly as for number fractions once everything is in factors.

Why it works

Only factors cancel

An algebraic fraction obeys every rule a number fraction does — and one above all: cancelling divides the whole top and the whole bottom, so only common FACTORS cancel. A term glued into a sum cannot be cancelled alone: in

\frac{x^2 + 5x}{x^2 - 25}

, striking out the

x^2

's is illegal (they're terms, not factors — test

x = 1

\frac{6}{-24}

, but "cancelling" gives

\frac{5}{-25}

; different, so wrong).

Factorise top, factorise bottom, THEN cancel

The legal route through the same fraction:

\frac{x^2 + 5x}{x^2 - 25} = \frac{x(x + 5)}{(x + 5)(x - 5)} = \frac{x}{x - 5}

Keep reading — free

The rest of the explanation, plus 2 worked examples you step through move by move.

Start free

Takes a minute — no card.