Algebraic fractions explained
Use this page to review the structure of algebraic fractions before working through your own example in the solver tool.
What this topic means and what to look for first.
Algebraic fractions work like number fractions, but they include variables in the numerator or denominator.
The main ideas are simplifying factors, finding common denominators, and checking restrictions.
One reliable route through the topic.
- 1Factorise the numerator and denominator where possible.
- 2Cancel only common factors, not separate terms.
- 3When adding or subtracting, find a common denominator first.
- 4Check whether any denominator would become 0.
See the method in action.
(x^2 + 5x) / x
- Factorise the numerator to x(x + 5).
- Cancel the common factor x.
- So the expression simplifies to x + 5, as long as x is not 0.
1/x + 1/2x
- Use 2x as the common denominator.
- Rewrite 1/x as 2/2x.
- So the sum is 3/2x.
Things that commonly send the method off track.
- Cancelling terms that are being added or subtracted instead of cancelling common factors.
- Ignoring values that make the denominator 0.
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A free account is the current follow-up route for returning to the solver beta and future guide updates as the public library grows.
Extra algebra revision resources
If you want more printed algebra practice after this page, these broader searches are a sensible next step.
Amazon
Algebra workbook and revision book search
Useful if you want more equation, factorising, and worked-example practice in one printed source.
View Algebra workbook and revision book searchAmazon
GCSE algebra practice resources search
A wider GCSE-style search if you want more mixed algebra questions beyond one online guide.
View GCSE algebra practice resources searchFound this useful?
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Short answers worth checking.
You can only cancel common factors, not terms that are separated by plus or minus signs.
A denominator cannot be 0, so you need to keep track of excluded values.
Continue with the next closely related topic.
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