Algebra Examples

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

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

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Step 2.1

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

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

Step 2.2

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

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Step 2.2.1

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

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

Step 2.2.2

Multiply $3$ by $2$ .

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

Step 2.3

Combine the numerators over the common denominator.

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

Step 2.4

Add $2$ and $1$ .

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

Step 2.5

Cancel the common factor of $3$ and $6$ .

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Step 2.5.1

Factor $3$ out of $3$ .

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

Step 2.5.2

Cancel the common factors.

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Step 2.5.2.1

Factor $3$ out of $6$ .

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

Step 2.5.2.2

Cancel the common factor.

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

Step 2.5.2.3

Rewrite the expression.

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

Step 3

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

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

Step 4

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

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

Step 5

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

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Step 5.1

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

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

Step 5.2

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

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

Step 5.3

Reorder the factors of $x \cdot 2$ .

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

Step 6

Combine the numerators over the common denominator.

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

Step 7

Set the numerator equal to zero.

$x - 2 = 0$

Step 8

Add $2$ to both sides of the equation.

$x = 2$