Algebra Examples

$\frac{x + 2}{4 x} - \frac{3}{2 x} = \frac{1}{8}$

Step 1

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

$\frac{x + 2}{4 x} - \frac{3}{2 x} - \frac{1}{8} = 0$

Step 2

Simplify $\frac{x + 2}{4 x} - \frac{3}{2 x} - \frac{1}{8}$ .

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Step 2.1

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

$\frac{x + 2}{4 x} - \frac{3}{2 x} \cdot \frac{2}{2} - \frac{1}{8} = 0$

Step 2.2

Write each expression with a common denominator of $4 x$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.2.1

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

$\frac{x + 2}{4 x} - \frac{3 \cdot 2}{2 x \cdot 2} - \frac{1}{8} = 0$

Step 2.2.2

Multiply $2$ by $2$ .

$\frac{x + 2}{4 x} - \frac{3 \cdot 2}{4 x} - \frac{1}{8} = 0$

Step 2.3

Combine the numerators over the common denominator.

$\frac{x + 2 - 3 \cdot 2}{4 x} - \frac{1}{8} = 0$

Step 2.4

Multiply $- 3$ by $2$ .

$\frac{x + 2 - 6}{4 x} - \frac{1}{8} = 0$

Step 2.5

Subtract $6$ from $2$ .

$\frac{x - 4}{4 x} - \frac{1}{8} = 0$

Step 2.6

To write $\frac{x - 4}{4 x}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{x - 4}{4 x} \cdot \frac{2}{2} - \frac{1}{8} = 0$

Step 2.7

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

$\frac{x - 4}{4 x} \cdot \frac{2}{2} - \frac{1}{8} \cdot \frac{x}{x} = 0$

Step 2.8

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

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Step 2.8.1

Multiply $\frac{x - 4}{4 x}$ by $\frac{2}{2}$ .

$\frac{(x - 4) \cdot 2}{4 x \cdot 2} - \frac{1}{8} \cdot \frac{x}{x} = 0$

Step 2.8.2

Multiply $2$ by $4$ .

$\frac{(x - 4) \cdot 2}{8 x} - \frac{1}{8} \cdot \frac{x}{x} = 0$

Step 2.8.3

Multiply $\frac{1}{8}$ by $\frac{x}{x}$ .

$\frac{(x - 4) \cdot 2}{8 x} - \frac{x}{8 x} = 0$

Step 2.9

Combine the numerators over the common denominator.

$\frac{(x - 4) \cdot 2 - x}{8 x} = 0$

Step 2.10

Simplify the numerator.

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Step 2.10.1

Apply the distributive property.

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

Step 2.10.2

Move $2$ to the left of $x$ .

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

Step 2.10.3

Multiply $- 4$ by $2$ .

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

Step 2.10.4

Subtract $x$ from $2 x$ .

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

Step 3

Set the numerator equal to zero.

$x - 8 = 0$

Step 4

Add $8$ to both sides of the equation.

$x = 8$