Algebra Examples

$\frac{8}{5 x} - \frac{2}{3 x} = \frac{4}{15}$

Step 1

Subtract $\frac{4}{15}$ from both sides of the equation.

$\frac{8}{5 x} - \frac{2}{3 x} - \frac{4}{15} = 0$

Step 2

Simplify $\frac{8}{5 x} - \frac{2}{3 x} - \frac{4}{15}$ .

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Step 2.1

To write $\frac{8}{5 x}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{8}{5 x} \cdot \frac{3}{3} - \frac{2}{3 x} - \frac{4}{15} = 0$

Step 2.2

To write $- \frac{2}{3 x}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{8}{5 x} \cdot \frac{3}{3} - \frac{2}{3 x} \cdot \frac{5}{5} - \frac{4}{15} = 0$

Step 2.3

Write each expression with a common denominator of $15 x$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.3.1

Multiply $\frac{8}{5 x}$ by $\frac{3}{3}$ .

$\frac{8 \cdot 3}{5 x \cdot 3} - \frac{2}{3 x} \cdot \frac{5}{5} - \frac{4}{15} = 0$

Step 2.3.2

Multiply $3$ by $5$ .

$\frac{8 \cdot 3}{15 x} - \frac{2}{3 x} \cdot \frac{5}{5} - \frac{4}{15} = 0$

Step 2.3.3

Multiply $\frac{2}{3 x}$ by $\frac{5}{5}$ .

$\frac{8 \cdot 3}{15 x} - \frac{2 \cdot 5}{3 x \cdot 5} - \frac{4}{15} = 0$

Step 2.3.4

Multiply $5$ by $3$ .

$\frac{8 \cdot 3}{15 x} - \frac{2 \cdot 5}{15 x} - \frac{4}{15} = 0$

Step 2.4

Combine the numerators over the common denominator.

$\frac{8 \cdot 3 - 2 \cdot 5}{15 x} - \frac{4}{15} = 0$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $8$ by $3$ .

$\frac{24 - 2 \cdot 5}{15 x} - \frac{4}{15} = 0$

Step 2.5.2

Multiply $- 2$ by $5$ .

$\frac{24 - 10}{15 x} - \frac{4}{15} = 0$

Step 2.5.3

Subtract $10$ from $24$ .

$\frac{14}{15 x} - \frac{4}{15} = 0$

Step 3

To write $- \frac{4}{15}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{14}{15 x} - \frac{4}{15} \cdot \frac{x}{x} = 0$

Step 4

Multiply $\frac{4}{15}$ by $\frac{x}{x}$ .

$\frac{14}{15 x} - \frac{4 x}{15 x} = 0$

Step 5

Combine the numerators over the common denominator.

$\frac{14 - 4 x}{15 x} = 0$

Step 6

Factor $2$ out of $14 - 4 x$ .

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Step 6.1

Factor $2$ out of $14$ .

$\frac{2 (7) - 4 x}{15 x} = 0$

Step 6.2

Factor $2$ out of $- 4 x$ .

$\frac{2 (7) + 2 (- 2 x)}{15 x} = 0$

Step 6.3

Factor $2$ out of $2 (7) + 2 (- 2 x)$ .

$\frac{2 (7 - 2 x)}{15 x} = 0$

Step 7

Set the numerator equal to zero.

$2 (7 - 2 x) = 0$

Step 8

Solve the equation for $x$ .

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Step 8.1

Divide each term in $2 (7 - 2 x) = 0$ by $2$ and simplify.

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Step 8.1.1

Divide each term in $2 (7 - 2 x) = 0$ by $2$ .

$\frac{2 (7 - 2 x)}{2} = \frac{0}{2}$

Step 8.1.2

Simplify the left side.

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Step 8.1.2.1

Cancel the common factor of $2$ .

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Step 8.1.2.1.1

Cancel the common factor.

$\frac{2 (7 - 2 x)}{2} = \frac{0}{2}$

Step 8.1.2.1.2

Divide $7 - 2 x$ by $1$ .

$7 - 2 x = \frac{0}{2}$

Step 8.1.3

Simplify the right side.

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Step 8.1.3.1

Divide $0$ by $2$ .

$7 - 2 x = 0$

Step 8.2

Subtract $7$ from both sides of the equation.

$- 2 x = - 7$

Step 8.3

Divide each term in $- 2 x = - 7$ by $- 2$ and simplify.

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Step 8.3.1

Divide each term in $- 2 x = - 7$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{- 7}{- 2}$

Step 8.3.2

Simplify the left side.

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Step 8.3.2.1

Cancel the common factor of $- 2$ .

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Step 8.3.2.1.1

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{- 7}{- 2}$

Step 8.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 7}{- 2}$

Step 8.3.3

Simplify the right side.

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Step 8.3.3.1

Dividing two negative values results in a positive value.

$x = \frac{7}{2}$