Find the Domain y=(x^2-4)/(2x+4)

$y = \frac{x^{2} - 4}{2 x + 4}$

Step 1

Set the denominator in $\frac{x^{2} - 4}{2 x + 4}$ equal to $0$ to find where the expression is undefined.

$2 x + 4 = 0$

Step 2

Solve for $x$ .

Subtract $4$ from both sides of the equation.

$2 x = - 4$

Divide each term in $2 x = - 4$ by $2$ and simplify.

Divide each term in $2 x = - 4$ by $2$ .

$\frac{2 x}{2} = \frac{- 4}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 4}{2}$

Divide $x$ by $1$ .

$x = \frac{- 4}{2}$

Simplify the right side.

Divide $- 4$ by $2$ .

$x = - 2$

Step 3

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

Interval Notation:

$(- \infty, - 2) \cup (- 2, \infty)$

Set-Builder Notation:

${x | x \neq - 2}$

Step 4