IGCSE Maths Algebraic Fractions Notes
Algebraic fractions have expressions in the numerator or denominator. Simplify by factorising and cancelling common factors.
Key concepts
- Simplifying
- Factorise top and bottom, then cancel common factors.
- Adding & subtracting
- Use a common denominator, just like numeric fractions.
- Solving
- Multiply through by the denominators to clear the fractions.
Key formulas
Common denominator
a/b + c/d = (ad + bc)/(bd)
Worked example
Simplify (x² − 9) / (x + 3).
- 1Factorise the numerator: x² − 9 = (x + 3)(x − 3).
- 2Cancel the common factor (x + 3).
- 3Write the simplified result.
Answer: x − 3
Common mistakes
✗ Cancelling terms that are not factors.
✓ Only cancel factors of the whole numerator and denominator, not individual terms.
✗ Forgetting a common denominator when adding.
✓ Rewrite both fractions over the same denominator first.
✗ Losing solutions that make the denominator zero.
✓ Exclude values that make any denominator zero.
Quick check
Try these, then reveal the answers.
Simplify 4x/2.Reveal answer
2x
Simplify (x² − 4)/(x − 2).Reveal answer
x + 2
Common denominator of 1/x and 1/y?Reveal answer
xy
Exam tips
- Always factorise fully before trying to cancel.
- Show the common denominator step clearly when adding or subtracting.
- State any restricted values where the denominator would be zero.
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Frequently asked questions
Can I cancel x in (x + 2)/x?+
No — x is not a factor of the whole numerator, so it cannot be cancelled.
How do I solve an equation with algebraic fractions?+
Multiply every term by the lowest common denominator to clear the fractions, then solve the resulting equation.
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