Find the Domain 13/(12x)=7/(3x)-5/12

$\frac{13}{12 x} = \frac{7}{3 x} - \frac{5}{12}$

Step 1

Set the denominator in $\frac{13}{12 x}$ equal to $0$ to find where the expression is undefined.

$12 x = 0$

Step 2

Divide each term in $12 x = 0$ by $12$ and simplify.

Divide each term in $12 x = 0$ by $12$ .

$\frac{12 x}{12} = \frac{0}{12}$

Simplify the left side.

Cancel the common factor of $12$ .

Cancel the common factor.

$\frac{12 x}{12} = \frac{0}{12}$

Divide $x$ by $1$ .

$x = \frac{0}{12}$

Simplify the right side.

Divide $0$ by $12$ .

$x = 0$

Step 3

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

Interval Notation:

$(- \infty, 0) \cup (0, \infty)$

Set-Builder Notation:

${x | x \neq 0}$

Step 4