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22nd May 2013

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# 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) = x2 + 3x      [after cancelling]
∴ 10x - 2x - 6 = x2 + 3x
∴ x2 - 5x + 6 = 0
∴ (x - 3)(x - 2) = 0
∴ either x = 3 or x = 2