Solve for x (x^2-36)/(6-x)=0

$\frac{x^{2} - 36}{6 - x} = 0$

Step 1

Set the numerator equal to zero.

$x^{2} - 36 = 0$

Step 2

Solve the equation for $x$ .

Add $36$ to both sides of the equation.

$x^{2} = 36$

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{36}$

Simplify $\pm \sqrt{36}$ .

Rewrite $36$ as $6^{2}$ .

$x = \pm \sqrt{6^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm 6$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x = 6$

Next, use the negative value of the $\pm$ to find the second solution.

$x = - 6$

The complete solution is the result of both the positive and negative portions of the solution.

$x = 6, - 6$

Step 3

Exclude the solutions that do not make $\frac{x^{2} - 36}{6 - x} = 0$ true.

$x = - 6$