Algebraic fractions
Y12 algebra: simplify, add/subtract with common denominator, multiply, divide.
Same operations as numerical fractions but with polynomials. Always factorise top and bottom first to spot cancellations.
Worked examples
(x² − 4) / (x − 2) = (x+2)(x-2)/(x-2) = x + 2 (x ≠ 2).
1/(x+1) + 1/(x-1) = 2x/(x²-1).
(x² / (x+1)) × ((x+1)/x) = x.
Frequently asked questions
Always state restrictions?
Yes — whatever made the original denominator zero. Examiners deduct marks for missing them.
How does this connect to partial fractions?
Reverse direction. Start with a single fraction, decompose into simpler ones.