Algebra Examples

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

Step 1

Subtract $\frac{1}{6}$ from both sides of the equation.

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

Step 2

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

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Step 2.1

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

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

Step 2.2

Write each expression with a common denominator of $x \cdot 2$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.2.1

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

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

Step 2.2.2

Move $2$ to the left of $x$ .

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

Step 2.3

Combine the numerators over the common denominator.

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

Step 2.4

Add $2$ and $1$ .

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

Step 3

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

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

Step 4

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

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

Step 5

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

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Step 5.1

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

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

Step 5.2

Multiply $3$ by $2$ .

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

Step 5.3

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

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

Step 6

Combine the numerators over the common denominator.

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

Step 7

Multiply $3$ by $3$ .

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

Step 8

Set the numerator equal to zero.

$9 - x = 0$

Step 9

Solve the equation for $x$ .

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Step 9.1

Subtract $9$ from both sides of the equation.

$- x = - 9$

Step 9.2

Divide each term in $- x = - 9$ by $- 1$ and simplify.

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Step 9.2.1

Divide each term in $- x = - 9$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 9}{- 1}$

Step 9.2.2

Simplify the left side.

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Step 9.2.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 9}{- 1}$

Step 9.2.2.2

Divide $x$ by $1$ .

$x = \frac{- 9}{- 1}$

Step 9.2.3

Simplify the right side.

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Step 9.2.3.1

Divide $- 9$ by $- 1$ .

$x = 9$