Algebraic fractions appear regularly in DSE Paper 1 Section A, typically worth 3–6 marks. This article provides a complete guide to simplifying algebraic fractions and performing the four operations: addition, subtraction, multiplication and division. You will learn the golden rule – factorise first, cancel second – and how to avoid common traps like cancelling across addition or subtraction. Worked examples, DSE exam techniques, practice questions are all included.
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Algebraic Fractions – Simplification & 4 Operations Complete Guide
Exercise
Simplify each expression completely.
- \(\displaystyle \frac{6x-12}{3}\)
- \(\displaystyle \frac{x^2-16}{x^2-8x+16}\)
- \(\displaystyle \frac{2x}{5} \times \frac{15}{4x^2}\)
- \(\displaystyle \frac{x+1}{x-2} \div \frac{x^2-1}{x^2-4x+4}\)
- \(\displaystyle \frac{2}{x} + \frac{5}{x}\)
- \(\displaystyle \frac{3}{x-2} + \frac{1}{x+1}\)
- \(\displaystyle \frac{4}{x} - \frac{2}{x-1}\)
- \(\displaystyle \frac{x^2+2x}{x^2-4} \times \frac{x-2}{x}\)
- \(\displaystyle \frac{x^2-3x+2}{x^2-1} \div \frac{x-2}{x+1}\)
- \(\displaystyle \frac{2}{x+3} - \frac{1}{x-3} + \frac{3}{x^2-9}\) A(2)-style
Answer Key
1. \(2x-4\)
2. \(\displaystyle \frac{x+4}{x-4}\)
3. \(\displaystyle \frac{3}{2x}\)
4. \(\displaystyle \frac{x-2}{x-1}\)
5. \(\displaystyle \frac{7}{x}\)
6. \(\displaystyle \frac{4x+1}{(x-2)(x+1)}\)
7. \(\displaystyle \frac{2x-4}{x(x-1)}\)
8. \(\displaystyle \frac{x+2}{x+2} = 1\) (for \(x \neq -2\))
9. \(\displaystyle 1\)
10. \(\displaystyle \frac{x-9}{(x-3)(x+3)}\)