Find the Domain 23/(10x)=7/(2x)-3/10

$\frac{23}{10 x} = \frac{7}{2 x} - \frac{3}{10}$

Step 1

Set the denominator in $\frac{23}{10 x}$ equal to $0$ to find where the expression is undefined.

$10 x = 0$

Step 2

Divide each term in $10 x = 0$ by $10$ and simplify.

Divide each term in $10 x = 0$ by $10$ .

$\frac{10 x}{10} = \frac{0}{10}$

Simplify the left side.

Cancel the common factor of $10$ .

Cancel the common factor.

$\frac{10 x}{10} = \frac{0}{10}$

Divide $x$ by $1$ .

$x = \frac{0}{10}$

Simplify the right side.

Divide $0$ by $10$ .

$x = 0$

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