Find the Excluded Values 3/x=3/(4x)+3

$\frac{3}{x} = \frac{3}{4 x} + 3$

Move all the expressions to the left side of the equation.

Subtract $\frac{3}{4 x}$ from both sides of the equation.

$\frac{3}{x} - \frac{3}{4 x} = 3$

Subtract $3$ from both sides of the equation.

$\frac{3}{x} - \frac{3}{4 x} - 3 = 0$

Simplify $\frac{3}{x} - \frac{3}{4 x} - 3$ .

To write $\frac{3}{x}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{3}{x} \cdot \frac{4}{4} - \frac{3}{4 x} - 3 = 0$

Write each expression with a common denominator of $x \cdot 4$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{3}{x}$ by $\frac{4}{4}$ .

$\frac{3 \cdot 4}{x \cdot 4} - \frac{3}{4 x} - 3 = 0$

Move $4$ to the left of $x$ .

$\frac{3 \cdot 4}{4 x} - \frac{3}{4 x} - 3 = 0$

Combine the numerators over the common denominator.

$\frac{3 \cdot 4 - 3}{4 x} - 3 = 0$

Simplify the numerator.

Multiply $3$ by $4$ .

$\frac{12 - 3}{4 x} - 3 = 0$

Subtract $3$ from $12$ .

$\frac{9}{4 x} - 3 = 0$

Set the denominator in $\frac{9}{4 x}$ equal to $0$ to find where the expression is undefined.

$4 x = 0$

Divide each term in $4 x = 0$ by $4$ and simplify.

Divide each term in $4 x = 0$ by $4$ .

$\frac{4 x}{4} = \frac{0}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{0}{4}$

Divide $x$ by $1$ .

$x = \frac{0}{4}$

Simplify the right side.

Divide $0$ by $4$ .

$x = 0$