Algebra Examples

$\frac{x}{5} - \frac{x}{6} = \frac{1}{3}$

Step 1

Simplify $\frac{x}{5} - \frac{x}{6}$ .

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Step 1.1

To write $\frac{x}{5}$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{x}{5} \cdot \frac{6}{6} - \frac{x}{6} = \frac{1}{3}$

Step 1.2

To write $- \frac{x}{6}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{x}{5} \cdot \frac{6}{6} - \frac{x}{6} \cdot \frac{5}{5} = \frac{1}{3}$

Step 1.3

Write each expression with a common denominator of $30$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{x}{5}$ by $\frac{6}{6}$ .

$\frac{x \cdot 6}{5 \cdot 6} - \frac{x}{6} \cdot \frac{5}{5} = \frac{1}{3}$

Step 1.3.2

Multiply $5$ by $6$ .

$\frac{x \cdot 6}{30} - \frac{x}{6} \cdot \frac{5}{5} = \frac{1}{3}$

Step 1.3.3

Multiply $\frac{x}{6}$ by $\frac{5}{5}$ .

$\frac{x \cdot 6}{30} - \frac{x \cdot 5}{6 \cdot 5} = \frac{1}{3}$

Step 1.3.4

Multiply $6$ by $5$ .

$\frac{x \cdot 6}{30} - \frac{x \cdot 5}{30} = \frac{1}{3}$

Step 1.4

Combine the numerators over the common denominator.

$\frac{x \cdot 6 - x \cdot 5}{30} = \frac{1}{3}$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Factor $x$ out of $x \cdot 6 - x \cdot 5$ .

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Step 1.5.1.1

Factor $x$ out of $x \cdot 6$ .

$\frac{x (6) - x \cdot 5}{30} = \frac{1}{3}$

Step 1.5.1.2

Factor $x$ out of $- x \cdot 5$ .

$\frac{x (6) + x (- 1 \cdot 5)}{30} = \frac{1}{3}$

Step 1.5.1.3

Factor $x$ out of $x (6) + x (- 1 \cdot 5)$ .

$\frac{x (6 - 1 \cdot 5)}{30} = \frac{1}{3}$

Step 1.5.2

Multiply $- 1$ by $5$ .

$\frac{x (6 - 5)}{30} = \frac{1}{3}$

Step 1.5.3

Subtract $5$ from $6$ .

$\frac{x \cdot 1}{30} = \frac{1}{3}$

Step 1.6

Multiply $x$ by $1$ .

$\frac{x}{30} = \frac{1}{3}$

Step 2

Multiply both sides of the equation by $30$ .

$30 \frac{x}{30} = 30 (\frac{1}{3})$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $30$ .

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Step 3.1.1.1

Cancel the common factor.

$30 \frac{x}{30} = 30 (\frac{1}{3})$

Step 3.1.1.2

Rewrite the expression.

$x = 30 (\frac{1}{3})$

Step 3.2

Simplify the right side.

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Step 3.2.1

Cancel the common factor of $3$ .

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Step 3.2.1.1

Factor $3$ out of $30$ .

$x = 3 (10) \frac{1}{3}$

Step 3.2.1.2

Cancel the common factor.

$x = 3 \cdot 10 \frac{1}{3}$

Step 3.2.1.3

Rewrite the expression.

$x = 10$