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Year 2 pushes algebraic fractions further, with more involved factorising and polynomial numerators. The four operations work exactly as with number fractions — the priority is always to factorise so you can cancel.
The big picture
Cancelling a common factor gives an equivalent expression only on the domain of the original fraction. In , both and are excluded even after the factor disappears. The simplified expression alone does not record the removable hole. For division by an algebraic fraction, the divisor must itself be defined and nonzero. Record these conditions before flipping it; the final simplified denominator may not display all the restrictions.
What you'll be able to do
Factorise the numerator and denominator fully, then cancel common (never individual terms). With quadratics this often means factorising both top and bottom first.
Tip — Cancelling is only valid on factors. (x² − 9)/(x + 3) works because x² − 9 factorises.
Factorise everything, cancel across the fractions, then multiply tops and bottoms. To divide, multiply by the reciprocal (keep–change–flip).
Find a common denominator (usually the product of the denominators, or their LCM), rewrite each fraction, then combine the numerators carefully — watch signs when subtracting.
Cancelling a common factor gives an equivalent expression only on the domain of the original fraction. In , both and are excluded even after the factor disappears. The simplified expression alone does not record the removable hole.
For division by an algebraic fraction, the divisor must itself be defined and nonzero. Record these conditions before flipping it; the final simplified denominator may not display all the restrictions.
Think like an examiner
Common misconceptions
Key results to remember
Key takeaways
Test yourself
Answer a few questions, then review anything you missed.
Start with the quiz above to check the key ideas. You can also choose another topic from the practice library.