Find the Excluded Values (x^2-16)/(x^2-81)

$\frac{x^{2} - 16}{x^{2} - 81}$

Step 1

Set the denominator in $\frac{x^{2} - 16}{x^{2} - 81}$ equal to $0$ to find where the expression is undefined.

$x^{2} - 81 = 0$

Step 2

Solve for $x$ .

Add $81$ to both sides of the equation.

$x^{2} = 81$

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

$x = \pm \sqrt{81}$

Simplify $\pm \sqrt{81}$ .

Rewrite $81$ as $9^{2}$ .

$x = \pm \sqrt{9^{2}}$

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

$x = \pm 9$

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.

$x = 9$

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

$x = - 9$

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

$x = 9, - 9$

Step 3

The equation is undefined where the denominator equals $0$ , the argument of a square root is less than $0$ , or the argument of a logarithm is less than or equal to $0$ .

$x = - 9, x = 9$

Step 4

Find the Excluded Values (x^2-16)/(x^2-81)

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