Solve by Factoring 1/6+1/9=1/x

$\frac{1}{6} + \frac{1}{9} = \frac{1}{x}$

Step 1

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

$\frac{1}{6} + \frac{1}{9} - \frac{1}{x} = 0$

Step 2

Simplify $\frac{1}{6} + \frac{1}{9} - \frac{1}{x}$ .

To write $\frac{1}{6}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{1}{6} \cdot \frac{3}{3} + \frac{1}{9} - \frac{1}{x} = 0$

To write $\frac{1}{9}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{1}{6} \cdot \frac{3}{3} + \frac{1}{9} \cdot \frac{2}{2} - \frac{1}{x} = 0$

Write each expression with a common denominator of $18$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{6}$ by $\frac{3}{3}$ .

$\frac{3}{6 \cdot 3} + \frac{1}{9} \cdot \frac{2}{2} - \frac{1}{x} = 0$

Multiply $6$ by $3$ .

$\frac{3}{18} + \frac{1}{9} \cdot \frac{2}{2} - \frac{1}{x} = 0$

Multiply $\frac{1}{9}$ by $\frac{2}{2}$ .

$\frac{3}{18} + \frac{2}{9 \cdot 2} - \frac{1}{x} = 0$

Multiply $9$ by $2$ .

$\frac{3}{18} + \frac{2}{18} - \frac{1}{x} = 0$

Combine the numerators over the common denominator.

$\frac{3 + 2}{18} - \frac{1}{x} = 0$

Add $3$ and $2$ .

$\frac{5}{18} - \frac{1}{x} = 0$

Step 3

To write $\frac{5}{18}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{5}{18} \cdot \frac{x}{x} - \frac{1}{x} = 0$

Step 4

To write $- \frac{1}{x}$ as a fraction with a common denominator, multiply by $\frac{18}{18}$ .

$\frac{5}{18} \cdot \frac{x}{x} - \frac{1}{x} \cdot \frac{18}{18} = 0$

Step 5

Write each expression with a common denominator of $18 x$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{5}{18}$ by $\frac{x}{x}$ .

$\frac{5 x}{18 x} - \frac{1}{x} \cdot \frac{18}{18} = 0$

Multiply $\frac{1}{x}$ by $\frac{18}{18}$ .

$\frac{5 x}{18 x} - \frac{18}{x \cdot 18} = 0$

Reorder the factors of $x \cdot 18$ .

$\frac{5 x}{18 x} - \frac{18}{18 x} = 0$

Step 6

Combine the numerators over the common denominator.

$\frac{5 x - 18}{18 x} = 0$

Step 7

Set the numerator equal to zero.

$5 x - 18 = 0$

Step 8

Solve the equation for $x$ .

Add $18$ to both sides of the equation.

$5 x = 18$

Divide each term in $5 x = 18$ by $5$ and simplify.

Divide each term in $5 x = 18$ by $5$ .

$\frac{5 x}{5} = \frac{18}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{18}{5}$

Divide $x$ by $1$ .

$x = \frac{18}{5}$

Solve by Factoring 1/6+1/9=1/x

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