Find the Domain (x+11)/(x^2-121)

$\frac{x + 11}{x^{2} - 121}$

Step 1

Set the denominator in $\frac{x + 11}{x^{2} - 121}$ equal to $0$ to find where the expression is undefined.

$x^{2} - 121 = 0$

Step 2

Solve for $x$ .

Add $121$ to both sides of the equation.

$x^{2} = 121$

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

$x = \pm \sqrt{121}$

Simplify $\pm \sqrt{121}$ .

Rewrite $121$ as $11^{2}$ .

$x = \pm \sqrt{11^{2}}$

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

$x = \pm 11$

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.

$x = 11$

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

$x = - 11$

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

$x = 11, - 11$

Step 3

The domain is all values of $x$ that make the expression defined.

Interval Notation:

$(- \infty, - 11) \cup (- 11, 11) \cup (11, \infty)$

Set-Builder Notation:

${x | x \neq 11, - 11}$

Step 4