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GCSE Maths > Algebra - Algebraic Fractions

Algebraic Fractions

Algebraic fractions are simply fractions with algebraic expressions on the top and/or bottom.

When adding or subtracting algebraic fractions, the first thing to do is to put them onto a common denominator (by cross multiplying).

e.g. 1 + 4
(x + 1) (x + 6)

= 1(x + 6) + 4(x + 1)
(x + 1)(x + 6)

= x + 6 + 4x + 4
(x + 1)(x + 6)

= 5x + 10
(x + 1)(x + 6)

Solving equations

When solving equations containing algebraic fractions, first multiply both sides by a number/expression which removes the fractions.

Example

Solve 10 - 2 = 1
(x + 3) x

multiply both sides by x(x + 3):
\ 10x(x + 3) - 2x(x + 3) = x(x + 3)
(x + 3) x

\ 10x - 2(x + 3) = x + 3x [after cancelling]
\ 10x - 2x - 6 = x + 3x
\ x - 5x + 6 = 0
\ (x - 3)(x - 2) = 0
\ either x = 3 or x = 2

Copyright Matthew Pinkney 2003

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