Algebra Examples

$\frac{2}{x} = \frac{1}{8 x} + 3$

Step 1

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

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Step 1.1

Subtract $\frac{1}{8 x}$ from both sides of the equation.

$\frac{2}{x} - \frac{1}{8 x} = 3$

Step 1.2

Subtract $3$ from both sides of the equation.

$\frac{2}{x} - \frac{1}{8 x} - 3 = 0$

Step 2

Simplify $\frac{2}{x} - \frac{1}{8 x} - 3$ .

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Step 2.1

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

$\frac{2}{x} \cdot \frac{8}{8} - \frac{1}{8 x} - 3 = 0$

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 $\frac{8}{8}$ .

$\frac{2 \cdot 8}{x \cdot 8} - \frac{1}{8 x} - 3 = 0$

Step 2.2.2

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

$\frac{2 \cdot 8}{8 x} - \frac{1}{8 x} - 3 = 0$

Step 2.3

Combine the numerators over the common denominator.

$\frac{2 \cdot 8 - 1}{8 x} - 3 = 0$

Step 2.4

Simplify the numerator.

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Step 2.4.1

Multiply $2$ by $8$ .

$\frac{16 - 1}{8 x} - 3 = 0$

Step 2.4.2

Subtract $1$ from $16$ .

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

Step 3

Set the denominator in $\frac{15}{8 x}$ equal to $0$ to find where the expression is undefined.

$8 x = 0$

Step 4

Divide each term in $8 x = 0$ by $8$ and simplify.

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Step 4.1

Divide each term in $8 x = 0$ by $8$ .

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

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $8$ .

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Step 4.2.1.1

Cancel the common factor.

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

Step 4.2.1.2

Divide $x$ by $1$ .

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

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $0$ by $8$ .

$x = 0$

Step 5