Find the Domain (x+7)/(x^2-49)

$\frac{x + 7}{x^{2} - 49}$

Step 1

Set the denominator in $\frac{x + 7}{x^{2} - 49}$ equal to $0$ to find where the expression is undefined.

$x^{2} - 49 = 0$

Step 2

Solve for $x$ .

Add $49$ to both sides of the equation.

$x^{2} = 49$

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

$x = \pm \sqrt{49}$

Simplify $\pm \sqrt{49}$ .

Rewrite $49$ as $7^{2}$ .

$x = \pm \sqrt{7^{2}}$

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

$x = \pm 7$

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.

$x = 7$

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

$x = - 7$

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

$x = 7, - 7$

Step 3

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

Interval Notation:

$(- \infty, - 7) \cup (- 7, 7) \cup (7, \infty)$

Set-Builder Notation:

${x | x \neq 7, - 7}$

Step 4