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Algebraic fractions
Algebraic fractions follow exactly the same rules as number fractions. Factorise first, always.
Simplifying
Factorise top and bottom, then cancel common factors (never single terms).
(x2 − 9)(x + 3) = (x + 3)(x − 3)(x + 3) = x − 3
(x2 − 9)(x + 3) = (x + 3)(x − 3)(x + 3) = x − 3
Adding and subtracting
Use a common denominator.
2x + 3(x + 1) = (2(x + 1) + 3x)(x(x + 1)) = (5x + 2)(x(x + 1))
2x + 3(x + 1) = (2(x + 1) + 3x)(x(x + 1)) = (5x + 2)(x(x + 1))
Multiplying and dividing
Multiply straight across. To divide, flip the second fraction.
Factorise and cancel before multiplying to keep it simple.
Factorise and cancel before multiplying to keep it simple.
Simplify (x2 + 5x + 6)(x2 − 4)
- Top: (x + 2)(x + 3)
- Bottom: (x + 2)(x − 2)
- Cancel (x + 2)
Answer: (x + 3)(x − 2)
Factorise first, then cancel whole brackets. Add and subtract with a common denominator. Multiply straight across; divide by flipping.
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