Algebra Examples

$(\frac{x}{3} - \frac{x}{4}) \div \frac{x}{12}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$(\frac{x}{3} - \frac{x}{4}) \frac{12}{x}$

Step 2

To write $\frac{x}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$(\frac{x}{3} \cdot \frac{4}{4} - \frac{x}{4}) \frac{12}{x}$

Step 3

To write $- \frac{x}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$(\frac{x}{3} \cdot \frac{4}{4} - \frac{x}{4} \cdot \frac{3}{3}) \frac{12}{x}$

Step 4

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{x}{3}$ by $\frac{4}{4}$ .

$(\frac{x \cdot 4}{3 \cdot 4} - \frac{x}{4} \cdot \frac{3}{3}) \frac{12}{x}$

Step 4.2

Multiply $3$ by $4$ .

$(\frac{x \cdot 4}{12} - \frac{x}{4} \cdot \frac{3}{3}) \frac{12}{x}$

Step 4.3

Multiply $\frac{x}{4}$ by $\frac{3}{3}$ .

$(\frac{x \cdot 4}{12} - \frac{x \cdot 3}{4 \cdot 3}) \frac{12}{x}$

Step 4.4

Multiply $4$ by $3$ .

$(\frac{x \cdot 4}{12} - \frac{x \cdot 3}{12}) \frac{12}{x}$

Step 5

Combine the numerators over the common denominator.

$\frac{x \cdot 4 - x \cdot 3}{12} \cdot \frac{12}{x}$

Step 6

Simplify the numerator.

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Step 6.1

Factor $x$ out of $x \cdot 4 - x \cdot 3$ .

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Step 6.1.1

Factor $x$ out of $x \cdot 4$ .

$\frac{x (4) - x \cdot 3}{12} \cdot \frac{12}{x}$

Step 6.1.2

Factor $x$ out of $- x \cdot 3$ .

$\frac{x (4) + x (- 1 \cdot 3)}{12} \cdot \frac{12}{x}$

Step 6.1.3

Factor $x$ out of $x (4) + x (- 1 \cdot 3)$ .

$\frac{x (4 - 1 \cdot 3)}{12} \cdot \frac{12}{x}$

Step 6.2

Multiply $- 1$ by $3$ .

$\frac{x (4 - 3)}{12} \cdot \frac{12}{x}$

Step 6.3

Subtract $3$ from $4$ .

$\frac{x \cdot 1}{12} \cdot \frac{12}{x}$

Step 7

Reduce the expression by cancelling the common factors.

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Step 7.1

Multiply $x$ by $1$ .

$\frac{x}{12} \cdot \frac{12}{x}$

Step 7.2

Cancel the common factor of $x$ .

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Step 7.2.1

Cancel the common factor.

$\frac{x}{12} \cdot \frac{12}{x}$

Step 7.2.2

Rewrite the expression.

$\frac{1}{12} \cdot 12$

Step 7.3

Cancel the common factor of $12$ .

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Step 7.3.1

Cancel the common factor.

$\frac{1}{12} \cdot 12$

Step 7.3.2

Rewrite the expression.

$1$