# How do you solve sqrt(x+1) = x-1 and find any extraneous solutions?

May 21, 2016

$x = 3$
 x=0

#### Explanation:

First, to remove the sqrt, square both sides of the equation, giving:

$x + 1 = {\left(x - 1\right)}^{2}$

Next, expand the equation out.

$x + 1 = {x}^{2} - 2 x + 1$

Simplify the equation combining like terms.

${x}^{2} - 3 x = 0$

$x \left(x - 3\right) = 0$

Now, you can solve for $x$:

$x = 0$
$x = 3$

However, if you solved it like this:

${x}^{2} - 3 x = 0$

${x}^{2} = 3 x$

$x = 3$

$x = 0$ would be a missing solution, this would be an extraneous solution.