Examples

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

Step 1

Move the negative in front of the fraction.

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

Step 2

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

$- \frac{2}{3 x} \cdot \frac{2}{2} - \frac{1}{2}$

Step 3

To write $- \frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{3 x}{3 x}$ .

$- \frac{2}{3 x} \cdot \frac{2}{2} - \frac{1}{2} \cdot \frac{3 x}{3 x}$

Step 4

Write each expression with a common denominator of $6 x$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

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

$- \frac{2 \cdot 2}{3 x \cdot 2} - \frac{1}{2} \cdot \frac{3 x}{3 x}$

Step 4.2

Multiply $2$ by $3$ .

$- \frac{2 \cdot 2}{6 x} - \frac{1}{2} \cdot \frac{3 x}{3 x}$

Step 4.3

Multiply $\frac{1}{2}$ by $\frac{3 x}{3 x}$ .

$- \frac{2 \cdot 2}{6 x} - \frac{3 x}{2 (3 x)}$

Step 4.4

Multiply $3$ by $2$ .

$- \frac{2 \cdot 2}{6 x} - \frac{3 x}{6 x}$

Step 5

Combine the numerators over the common denominator.

$\frac{- 2 \cdot 2 - 3 x}{6 x}$

Step 6

Multiply $- 2$ by $2$ .

$\frac{- 4 - 3 x}{6 x}$

Step 7

Rewrite $- 4$ as $- 1 (4)$ .

$\frac{- 1 (4) - 3 x}{6 x}$

Step 8

Factor $- 1$ out of $- 3 x$ .

$\frac{- 1 (4) - (3 x)}{6 x}$

Step 9

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

$\frac{- 1 (4 + 3 x)}{6 x}$

Step 10

Move the negative in front of the fraction.

$- \frac{4 + 3 x}{6 x}$

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