# What is extraneous solution?

Nov 9, 2016

See explanation...

#### Explanation:

If you are given a problem A to solve, you may convert it by a set of steps into a problem B which is easier to solve. Some of the solutions of problem B may be solutions of the original problem, but some may not. The ones which are not are known as extraneous solutions.

This can happen if you multiply an equation through by an expression that may take the value $0$, or if you square both sides of an equation, etc.

For example, suppose you are asked to solve:

$\frac{{x}^{2} - 4}{x - 2} = 0$

Multiplying both sides of the equation by $\left(x - 2\right)$ you get:

${x}^{2} - 4 = 0$

which has solutions $x = 2$ and $x = - 2$

The value $x = - 2$ is a solution of the original equation, but $x = 2$ is not since it results in division by $0$.