Algebra Examples

$\frac{1}{6} + \frac{1}{7} = \frac{1}{x}$

Step 1

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

$\frac{1}{6} + \frac{1}{7} - \frac{1}{x} = 0$

Step 2

Simplify $\frac{1}{6} + \frac{1}{7} - \frac{1}{x}$ .

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Step 2.1

To write $\frac{1}{6}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{1}{6} \cdot \frac{7}{7} + \frac{1}{7} - \frac{1}{x} = 0$

Step 2.2

To write $\frac{1}{7}$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{1}{6} \cdot \frac{7}{7} + \frac{1}{7} \cdot \frac{6}{6} - \frac{1}{x} = 0$

Step 2.3

Write each expression with a common denominator of $42$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.3.1

Multiply $\frac{1}{6}$ by $\frac{7}{7}$ .

$\frac{7}{6 \cdot 7} + \frac{1}{7} \cdot \frac{6}{6} - \frac{1}{x} = 0$

Step 2.3.2

Multiply $6$ by $7$ .

$\frac{7}{42} + \frac{1}{7} \cdot \frac{6}{6} - \frac{1}{x} = 0$

Step 2.3.3

Multiply $\frac{1}{7}$ by $\frac{6}{6}$ .

$\frac{7}{42} + \frac{6}{7 \cdot 6} - \frac{1}{x} = 0$

Step 2.3.4

Multiply $7$ by $6$ .

$\frac{7}{42} + \frac{6}{42} - \frac{1}{x} = 0$

Step 2.4

Combine the numerators over the common denominator.

$\frac{7 + 6}{42} - \frac{1}{x} = 0$

Step 2.5

Add $7$ and $6$ .

$\frac{13}{42} - \frac{1}{x} = 0$

Step 3

To write $\frac{13}{42}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{13}{42} \cdot \frac{x}{x} - \frac{1}{x} = 0$

Step 4

To write $- \frac{1}{x}$ as a fraction with a common denominator, multiply by $\frac{42}{42}$ .

$\frac{13}{42} \cdot \frac{x}{x} - \frac{1}{x} \cdot \frac{42}{42} = 0$

Step 5

Write each expression with a common denominator of $42 x$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.1

Multiply $\frac{13}{42}$ by $\frac{x}{x}$ .

$\frac{13 x}{42 x} - \frac{1}{x} \cdot \frac{42}{42} = 0$

Step 5.2

Multiply $\frac{1}{x}$ by $\frac{42}{42}$ .

$\frac{13 x}{42 x} - \frac{42}{x \cdot 42} = 0$

Step 5.3

Reorder the factors of $x \cdot 42$ .

$\frac{13 x}{42 x} - \frac{42}{42 x} = 0$

Step 6

Combine the numerators over the common denominator.

$\frac{13 x - 42}{42 x} = 0$

Step 7

Set the numerator equal to zero.

$13 x - 42 = 0$

Step 8

Solve the equation for $x$ .

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Step 8.1

Add $42$ to both sides of the equation.

$13 x = 42$

Step 8.2

Divide each term in $13 x = 42$ by $13$ and simplify.

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Step 8.2.1

Divide each term in $13 x = 42$ by $13$ .

$\frac{13 x}{13} = \frac{42}{13}$

Step 8.2.2

Simplify the left side.

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Step 8.2.2.1

Cancel the common factor of $13$ .

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Step 8.2.2.1.1

Cancel the common factor.

$\frac{13 x}{13} = \frac{42}{13}$

Step 8.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{42}{13}$