# 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) = x^{2} + 3x [after cancelling]

∴ 10x - 2x - 6 = x^{2} + 3x

∴ x^{2} - 5x + 6 = 0

∴ (x - 3)(x - 2) = 0

∴ either __x = 3 or x = 2__