Algebra Examples

$\frac{2}{x} = \frac{13}{8 x} + 3$

Step 1

Move all the expressions to the left side of the equation.

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Step 1.1

Subtract $\frac{13}{8 x}$ from both sides of the equation.

$\frac{2}{x} - \frac{13}{8 x} = 3$

Step 1.2

Subtract $3$ from both sides of the equation.

$\frac{2}{x} - \frac{13}{8 x} - 3 = 0$

Step 2

Simplify $\frac{2}{x} - \frac{13}{8 x} - 3$ .

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Step 2.1

To write $\frac{2}{x}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{2}{x} \cdot \frac{8}{8} - \frac{13}{8 x} - 3 = 0$

Step 2.2

Write each expression with a common denominator of $x \cdot 8$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.2.1

Multiply $\frac{2}{x}$ by $\frac{8}{8}$ .

$\frac{2 \cdot 8}{x \cdot 8} - \frac{13}{8 x} - 3 = 0$

Step 2.2.2

Move $8$ to the left of $x$ .

$\frac{2 \cdot 8}{8 x} - \frac{13}{8 x} - 3 = 0$

Step 2.3

Combine the numerators over the common denominator.

$\frac{2 \cdot 8 - 13}{8 x} - 3 = 0$

Step 2.4

Simplify the numerator.

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Step 2.4.1

Multiply $2$ by $8$ .

$\frac{16 - 13}{8 x} - 3 = 0$

Step 2.4.2

Subtract $13$ from $16$ .

$\frac{3}{8 x} - 3 = 0$

Step 3

Factor $3$ out of $\frac{3}{8 x} - 3$ .

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Step 3.1

Factor $3$ out of $\frac{3}{8 x}$ .

$3 (\frac{1}{8 x}) - 3 = 0$

Step 3.2

Factor $3$ out of $- 3$ .

$3 (\frac{1}{8 x}) + 3 \cdot - 1 = 0$

Step 3.3

Factor $3$ out of $3 \frac{1}{8 x} + 3 \cdot - 1$ .

$3 (\frac{1}{8 x} - 1) = 0$

Step 4

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{8 x}{8 x}$ .

$3 (\frac{1}{8 x} - 1 \cdot \frac{8 x}{8 x}) = 0$

Step 5

Combine $- 1$ and $\frac{8 x}{8 x}$ .

$3 (\frac{1}{8 x} + \frac{- (8 x)}{8 x}) = 0$

Step 6

Combine the numerators over the common denominator.

$3 (\frac{1 - (8 x)}{8 x}) = 0$

Step 7

Remove parentheses.

$3 (\frac{1 - 1 \cdot (8 x)}{8 x}) = 0$

Step 8

Multiply $- 1$ by $8$ .

$3 (\frac{1 - 8 x}{8 x}) = 0$

Step 9

Combine $3$ and $\frac{1 - 8 x}{8 x}$ .

$\frac{3 (1 - 8 x)}{8 x} = 0$

Step 10

Set the numerator equal to zero.

$3 (1 - 8 x) = 0$

Step 11

Solve the equation for $x$ .

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Step 11.1

Divide each term in $3 (1 - 8 x) = 0$ by $3$ and simplify.

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Step 11.1.1

Divide each term in $3 (1 - 8 x) = 0$ by $3$ .

$\frac{3 (1 - 8 x)}{3} = \frac{0}{3}$

Step 11.1.2

Simplify the left side.

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Step 11.1.2.1

Cancel the common factor of $3$ .

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Step 11.1.2.1.1

Cancel the common factor.

$\frac{3 (1 - 8 x)}{3} = \frac{0}{3}$

Step 11.1.2.1.2

Divide $1 - 8 x$ by $1$ .

$1 - 8 x = \frac{0}{3}$

Step 11.1.3

Simplify the right side.

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Step 11.1.3.1

Divide $0$ by $3$ .

$1 - 8 x = 0$

Step 11.2

Subtract $1$ from both sides of the equation.

$- 8 x = - 1$

Step 11.3

Divide each term in $- 8 x = - 1$ by $- 8$ and simplify.

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Step 11.3.1

Divide each term in $- 8 x = - 1$ by $- 8$ .

$\frac{- 8 x}{- 8} = \frac{- 1}{- 8}$

Step 11.3.2

Simplify the left side.

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Step 11.3.2.1

Cancel the common factor of $- 8$ .

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Step 11.3.2.1.1

Cancel the common factor.

$\frac{- 8 x}{- 8} = \frac{- 1}{- 8}$

Step 11.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 1}{- 8}$

Step 11.3.3

Simplify the right side.

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Step 11.3.3.1

Dividing two negative values results in a positive value.

$x = \frac{1}{8}$