Algebraic fractions are an important part of GCSE Maths and appear frequently in questions from exam boards like AQA, Edexcel, and OCR. Whether you’re simplifying, adding and subtracting, or solving equations involving algebraic fractions, mastering these skills can give you a significant edge. This complete guide breaks down each concept step-by-step with examples, tips, and exam-style practice questions.
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🔹 What Are Algebraic Fractions?
An algebraic fraction is simply a fraction that contains algebraic expressions in the numerator, denominator, or both. Just like numeric fractions, they follow rules for simplification, operations, and solving equations.
✅ Examples:
- x/x+2
- (2x+3)/4
- (x-1)/(x+1)
Understanding how to simplify and manipulate these expressions is key to solving more complex algebra problems.
🔸 Simplifying Algebraic Fractions
To simplify algebraic fractions, look for common factors in the numerator and denominator. Sometimes, you’ll need to factorise expressions to identify these.
📌 Example 1:
Here, we factorised the numerator using the difference of squares.
📌 Example 2:
The common factor 2x cancels out.
🔸 Adding & Subtracting Algebraic Fractions
You must find a common denominator before adding or subtracting algebraic fractions, just like with numeric fractions.
📌 Example:
1/x + 2/(x+1) => LCM is x(x+1)
{(x+1)+2x}/x(x+1) = (3x+1)/x(x+1)
Make sure to simplify your answer if possible.
🔸 Solving Equations Involving Algebraic Fractions
To solve equations with algebraic fractions:
- Find a common denominator for all terms
- Multiply every term to eliminate denominators
- Solve the resulting equation like a normal algebra problem
📌 Example:
Solve 1/x = (3/x+2) Cross-multiplying:
1(x+2) = 3x => x+2 = 3x => 2 = 2x => x=1
Always check that your solution doesn’t make any denominator zero.
🧠 Top Exam Tips for Algebraic Fractions
- Factorise completely before simplifying
- Always find the lowest common denominator (LCD) for adding/subtracting
- Avoid cancelling terms incorrectly—only cancel full factors
- Check restrictions (e.g., x ≠ 0 or x ≠ -1) to avoid invalid solutions
- Practice with past paper questions from AQA, Edexcel, and OCR
📝 Practice Question
- Simplify (X^2 – 4)/(x-2)
- Add 1/x + (1/x+3)
- Solve (x+1)/2 = 3/(x+1)
- Solve 2/x – (1/x+1) = 1
These practice problems are typical of those found in GCSE Maths exam questions.
✅ Final Thoughts
Algebraic fractions require careful handling but become manageable with consistent practice. By understanding simplification, common denominators, and solving techniques, you’ll become confident in tackling these questions under exam pressure.
For step-by-step tutorials, revision worksheets, and guided lessons tailored to your exam board, visit GCSE Maths Tutor and become an algebra pro.
