## 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).

The video below shows you how to calculate algebraic fractions.

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