Solve by Factoring 2/(3x)+1/6=4/(3x)

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

Step 1

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

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

Step 2

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

Combine the numerators over the common denominator.

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

Subtract $4$ from $2$ .

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

Move the negative in front of the fraction.

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

Step 3

To write $- \frac{2}{3 x}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 4

To write $\frac{1}{6}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

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

Step 5

Write each expression with a common denominator of $6 x$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{2}{3 x}$ by $\frac{2}{2}$ .

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

Multiply $2$ by $3$ .

$- \frac{2 \cdot 2}{6 x} + \frac{1}{6} \cdot \frac{x}{x} = 0$

Multiply $\frac{1}{6}$ by $\frac{x}{x}$ .

$- \frac{2 \cdot 2}{6 x} + \frac{x}{6 x} = 0$

Step 6

Combine the numerators over the common denominator.

$\frac{- 2 \cdot 2 + x}{6 x} = 0$

Step 7

Multiply $- 2$ by $2$ .

$\frac{- 4 + x}{6 x} = 0$

Step 8

Set the numerator equal to zero.

$- 4 + x = 0$

Step 9

Add $4$ to both sides of the equation.

$x = 4$