Find the Domain 1/(6x)=7/(2x)-5/6

$\frac{1}{6 x} = \frac{7}{2 x} - \frac{5}{6}$

Step 1

Set the denominator in $\frac{1}{6 x}$ equal to $0$ to find where the expression is undefined.

$6 x = 0$

Step 2

Divide each term in $6 x = 0$ by $6$ and simplify.

Divide each term in $6 x = 0$ by $6$ .

$\frac{6 x}{6} = \frac{0}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} = \frac{0}{6}$

Divide $x$ by $1$ .

$x = \frac{0}{6}$

Simplify the right side.

Divide $0$ by $6$ .

$x = 0$

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