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__