Algebraic Fractions
Simplify algebraic fractions
Simplifying Algebraic Fractions
An algebraic fraction has variables in the numerator, denominator or both. To simplify, factorise the numerator and denominator, then cancel common factors.
Example
Factorising and Cancelling
Simplify: (2x + 6) / (x + 3)
Factorise numerator: 2(x + 3)
Cancel (x + 3): = 2/1 = 2
Simplify: (x² − 9) / (x + 3)
Factorise: (x+3)(x−3) / (x+3)
Cancel: = x − 3
Example
Multiplying Algebraic Fractions
(x/4) × (8/x²)
= 8x / 4x²
= 2/x (cancel 4 and x)
(x²−4)/(x+1) × (x+1)/(x−2)
= (x+2)(x−2)/(x+1) × (x+1)/(x−2)
= x + 2
Note
Remember
Always factorise before cancelling. You can only cancel factors (multiplied), never terms (added). State restrictions: the denominator cannot equal zero.
Key Vocabulary
Algebraic fractionA fraction containing variables
FactoriseWrite an expression as a product of factors
CancelDivide top and bottom by a common factor
RestrictionValues of the variable that make the denominator zero (not allowed)
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