Finite Math Examples

$\frac{x}{3} - \frac{x}{4} = \frac{5}{4}$

Step 1

Simplify $\frac{x}{3} - \frac{x}{4}$ .

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Step 1.1

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

$\frac{x}{3} \cdot \frac{4}{4} - \frac{x}{4} = \frac{5}{4}$

Step 1.2

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

$\frac{x}{3} \cdot \frac{4}{4} - \frac{x}{4} \cdot \frac{3}{3} = \frac{5}{4}$

Step 1.3

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

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Step 1.3.1

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

$\frac{x \cdot 4}{3 \cdot 4} - \frac{x}{4} \cdot \frac{3}{3} = \frac{5}{4}$

Step 1.3.2

Multiply $3$ by $4$ .

$\frac{x \cdot 4}{12} - \frac{x}{4} \cdot \frac{3}{3} = \frac{5}{4}$

Step 1.3.3

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

$\frac{x \cdot 4}{12} - \frac{x \cdot 3}{4 \cdot 3} = \frac{5}{4}$

Step 1.3.4

Multiply $4$ by $3$ .

$\frac{x \cdot 4}{12} - \frac{x \cdot 3}{12} = \frac{5}{4}$

Step 1.4

Combine the numerators over the common denominator.

$\frac{x \cdot 4 - x \cdot 3}{12} = \frac{5}{4}$

Step 1.5

Simplify the numerator.

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Step 1.5.1

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

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Step 1.5.1.1

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

$\frac{x (4) - x \cdot 3}{12} = \frac{5}{4}$

Step 1.5.1.2

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

$\frac{x (4) + x (- 1 \cdot 3)}{12} = \frac{5}{4}$

Step 1.5.1.3

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

$\frac{x (4 - 1 \cdot 3)}{12} = \frac{5}{4}$

Step 1.5.2

Multiply $- 1$ by $3$ .

$\frac{x (4 - 3)}{12} = \frac{5}{4}$

Step 1.5.3

Subtract $3$ from $4$ .

$\frac{x \cdot 1}{12} = \frac{5}{4}$

Step 1.6

Multiply $x$ by $1$ .

$\frac{x}{12} = \frac{5}{4}$

Step 2

Multiply both sides of the equation by $12$ .

$12 \frac{x}{12} = 12 (\frac{5}{4})$

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 $12$ .

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Step 3.1.1.1

Cancel the common factor.

$12 \frac{x}{12} = 12 (\frac{5}{4})$

Step 3.1.1.2

Rewrite the expression.

$x = 12 (\frac{5}{4})$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $12 (\frac{5}{4})$ .

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Step 3.2.1.1

Cancel the common factor of $4$ .

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Step 3.2.1.1.1

Factor $4$ out of $12$ .

$x = 4 (3) \frac{5}{4}$

Step 3.2.1.1.2

Cancel the common factor.

$x = 4 \cdot 3 \frac{5}{4}$

Step 3.2.1.1.3

Rewrite the expression.

$x = 3 \cdot 5$

Step 3.2.1.2

Multiply $3$ by $5$ .

$x = 15$