Algebraic Fractions
Year 11 (IGCSE) 📊 Algebra Simplify, add, subtract and solve equations with algebraic fractions.
➗ Simplifying Algebraic Fractions
Simplify by factorising both numerator and denominator fully, then cancelling any common factors.
Example: $\frac{x^2 - 9}{x^2 + 2x - 3} = \frac{(x+3)(x-3)}{(x+3)(x-1)} = \frac{x-3}{x-1}$
Only cancel common factors, never individual terms from a sum or difference. $\frac{x+3}{x+5} \neq \frac{3}{5}$
➕ Adding and Subtracting Algebraic Fractions
Find a common denominator, adjust numerators, combine, then simplify.
- Factorise each denominator.
- Write the LCM as the common denominator.
- Rewrite each fraction over the common denominator.
- Combine the numerators.
- Simplify the result if possible.
Example: $\frac{3}{x+2} + \frac{1}{x-1} = \frac{3(x-1) + (x+2)}{(x+2)(x-1)} = \frac{4x-1}{(x+2)(x-1)}$
✖️ Multiplying and Dividing Algebraic Fractions
Multiply numerators and denominators separately. For division, flip the second fraction first.
⚡ Rules
$$\frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd} \qquad \frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} = \frac{ad}{bc}$$Example: $\frac{x^2+x}{x-2} \div \frac{x+1}{x^2-4} = \frac{x(x+1)}{x-2} \times \frac{(x+2)(x-2)}{x+1} = x(x+2)$
Ready to test yourself? Click the Quiz tab above to answer questions on this topic!
Interactive Demonstration — Algebraic Fractions
🎬
Interactive demonstration available in the Calculator tab!
➗ Algebraic Fraction Tool
🧮
Use the interactive inputs above to explore this topic!
Calculator tools are loading for all Cambridge topics.