Solve by Factoring 1/3-1/6=1/x

$\frac{1}{3} - \frac{1}{6} = \frac{1}{x}$

Step 1

Subtract $\frac{1}{x}$ from both sides of the equation.

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

Step 2

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

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

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

Multiply $\frac{1}{3}$ by $\frac{2}{2}$ .

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

Multiply $3$ by $2$ .

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

Combine the numerators over the common denominator.

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

Subtract $1$ from $2$ .

$\frac{1}{6} - \frac{1}{x} = 0$

Step 3

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

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

Step 4

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

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

Step 5

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

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

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

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

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

Reorder the factors of $x \cdot 6$ .

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

Step 6

Combine the numerators over the common denominator.

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

Step 7

Set the numerator equal to zero.

$x - 6 = 0$

Step 8

Add $6$ to both sides of the equation.

$x = 6$