# Equations involving algebraic fractions

**Equations involving algebraic fractions**

In situations with equations which involve algebraic fractions, the following steps should be taken to solve them. For example:

(multiply out by the product of denominators, multiply by *x*(*x* + 4))

*x* + 4 + 5*x* = 2*x*(*x* + 4) – (expand the brackets and simplify)

6*x* + 4 = 2*x²* + 8*x* – (collect the terms on the right hand side)

0 = 2*x²* + 2*x – *4 – (divide all by two)

0 = *x²* + *x – 2 – *(factorise)

0 = (*x + *2)(*x – *1)

*x* = -2 or *x* = 1