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Simplifying Algebraic Fractions Flashcards
GCSE Mathematics (Edexcel) 1MA1
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Algebraic fraction
A fraction where the numerator, denominator, or both contain algebraic expressions.
Simplifying algebraic fractions
Divide the numerator and denominator by their highest common factor (HCF).
Factorising before simplifying
Factorise the numerator and denominator first to identify common factors.
Cancelling common factors
Cancel out any common factors in the numerator and denominator to simplify the fraction.
Example: Simplify (x^2 - 9) / (x^2 - 6x + 9)
Factorise: (x + 3)(x - 3) / (x - 3)(x - 3). Cancel (x - 3). Result: (x + 3) / (x - 3).
Simplifying with numbers and variables
Treat numbers and variables separately. Simplify numerical coefficients and cancel common variable factors.
Restrictions on variables
State any restrictions where the denominator equals zero, as division by zero is undefined.
Example: Simplify (2x^2 + 4x) / (4x)
Factorise: 2x(x + 2) / 4x. Cancel 2x. Result: (x + 2) / 2.
Multiplying algebraic fractions
Multiply the numerators together and the denominators together, then simplify the result.
Dividing algebraic fractions
Flip the second fraction (reciprocal), then multiply as usual and simplify.
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