Find the Excluded Values 2/(3x)+1/4=46/(6x)-1/3

$\frac{2}{3 x} + \frac{1}{4} = \frac{46}{6 x} - \frac{1}{3}$

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

Subtract $\frac{46}{6 x}$ from both sides of the equation.

$\frac{2}{3 x} + \frac{1}{4} - \frac{46}{6 x} = - \frac{1}{3}$

Add $\frac{1}{3}$ to both sides of the equation.

$\frac{2}{3 x} + \frac{1}{4} - \frac{46}{6 x} + \frac{1}{3} = 0$

Simplify $\frac{2}{3 x} + \frac{1}{4} - \frac{46}{6 x} + \frac{1}{3}$ .

Cancel the common factor of $46$ and $6$ .

Factor $2$ out of $46$ .

$\frac{2}{3 x} + \frac{1}{4} - \frac{2 (23)}{6 x} + \frac{1}{3} = 0$

Cancel the common factors.

Factor $2$ out of $6 x$ .

$\frac{2}{3 x} + \frac{1}{4} - \frac{2 (23)}{2 (3 x)} + \frac{1}{3} = 0$

Cancel the common factor.

$\frac{2}{3 x} + \frac{1}{4} - \frac{2 \cdot 23}{2 (3 x)} + \frac{1}{3} = 0$

Rewrite the expression.

$\frac{2}{3 x} + \frac{1}{4} - \frac{23}{3 x} + \frac{1}{3} = 0$

Combine the numerators over the common denominator.

$\frac{2 - 23}{3 x} + \frac{1}{4} + \frac{1}{3} = 0$

Subtract $23$ from $2$ .

$\frac{- 21}{3 x} + \frac{1}{4} + \frac{1}{3} = 0$

Simplify each term.

Cancel the common factor of $- 21$ and $3$ .

Factor $3$ out of $- 21$ .

$\frac{3 \cdot - 7}{3 x} + \frac{1}{4} + \frac{1}{3} = 0$

Cancel the common factors.

Factor $3$ out of $3 x$ .

$\frac{3 \cdot - 7}{3 (x)} + \frac{1}{4} + \frac{1}{3} = 0$

Cancel the common factor.

$\frac{3 \cdot - 7}{3 x} + \frac{1}{4} + \frac{1}{3} = 0$

Rewrite the expression.

$\frac{- 7}{x} + \frac{1}{4} + \frac{1}{3} = 0$

Move the negative in front of the fraction.

$- \frac{7}{x} + \frac{1}{4} + \frac{1}{3} = 0$

To write $\frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{7}{x} + \frac{1}{4} \cdot \frac{3}{3} + \frac{1}{3} = 0$

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- \frac{7}{x} + \frac{1}{4} \cdot \frac{3}{3} + \frac{1}{3} \cdot \frac{4}{4} = 0$

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{4}$ by $\frac{3}{3}$ .

$- \frac{7}{x} + \frac{3}{4 \cdot 3} + \frac{1}{3} \cdot \frac{4}{4} = 0$

Multiply $4$ by $3$ .

$- \frac{7}{x} + \frac{3}{12} + \frac{1}{3} \cdot \frac{4}{4} = 0$

Multiply $\frac{1}{3}$ by $\frac{4}{4}$ .

$- \frac{7}{x} + \frac{3}{12} + \frac{4}{3 \cdot 4} = 0$

Multiply $3$ by $4$ .

$- \frac{7}{x} + \frac{3}{12} + \frac{4}{12} = 0$

Combine the numerators over the common denominator.

$- \frac{7}{x} + \frac{3 + 4}{12} = 0$

Add $3$ and $4$ .

$- \frac{7}{x} + \frac{7}{12} = 0$

Set the denominator in $\frac{7}{x}$ equal to $0$ to find where the expression is undefined.

$x = 0$

Find the Excluded Values 2/(3x)+1/4=46/(6x)-1/3

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