Algebraic fractions
Simplify, add/subtract (common denominator), multiply, divide (multiply by reciprocal).
Higher-tier algebra. Same rules as numerical fractions but with x's. Always factorise first to spot cancellation opportunities.
Worked examples
(x² − 9)/(x + 3) = (x+3)(x−3)/(x+3) = x − 3. (x ≠ −3)
1/(x − 1) + 1/(x + 2) = (2x + 1) / [(x−1)(x+2)].
(x/2) ÷ (3/x) = (x/2) × (x/3) = x²/6.
Frequently asked questions
Domain restrictions?
Whatever made the original denominator zero is excluded: x ≠ −3 in the first example. Higher exams test this.
Always factorise first?
Yes — cancellation is the goal, and it requires identifying common factors.