Find the Domain (x-4)/(2x-6)

$\frac{x - 4}{2 x - 6}$

Step 1

Set the denominator in $\frac{x - 4}{2 x - 6}$ equal to $0$ to find where the expression is undefined.

$2 x - 6 = 0$

Step 2

Solve for $x$ .

Add $6$ to both sides of the equation.

$2 x = 6$

Divide each term in $2 x = 6$ by $2$ and simplify.

Divide each term in $2 x = 6$ by $2$ .

$\frac{2 x}{2} = \frac{6}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{6}{2}$

Divide $x$ by $1$ .

$x = \frac{6}{2}$

Simplify the right side.

Divide $6$ by $2$ .

$x = 3$

Step 3

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

Interval Notation:

$(- \infty, 3) \cup (3, \infty)$

Set-Builder Notation:

${x | x \neq 3}$

Step 4