Pre-Algebra Examples

$- \frac{1}{6 x} + \frac{1}{4}$

Step 1

To write $- \frac{1}{6 x}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{1}{6 x} \cdot \frac{2}{2} + \frac{1}{4}$

Step 2

To write $\frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{3 x}{3 x}$ .

$- \frac{1}{6 x} \cdot \frac{2}{2} + \frac{1}{4} \cdot \frac{3 x}{3 x}$

Step 3

Write each expression with a common denominator of $12 x$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{1}{6 x}$ by $\frac{2}{2}$ .

$- \frac{2}{6 x \cdot 2} + \frac{1}{4} \cdot \frac{3 x}{3 x}$

Step 3.2

Multiply $2$ by $6$ .

$- \frac{2}{12 x} + \frac{1}{4} \cdot \frac{3 x}{3 x}$

Step 3.3

Multiply $\frac{1}{4}$ by $\frac{3 x}{3 x}$ .

$- \frac{2}{12 x} + \frac{3 x}{4 (3 x)}$

Step 3.4

Multiply $3$ by $4$ .

$- \frac{2}{12 x} + \frac{3 x}{12 x}$

Step 4

Combine the numerators over the common denominator.

$\frac{- 2 + 3 x}{12 x}$

Step 5

Rewrite $- 2$ as $- 1 (2)$ .

$\frac{- 1 (2) + 3 x}{12 x}$

Step 6

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

$\frac{- 1 (2) - (- 3 x)}{12 x}$

Step 7

Factor $- 1$ out of $- 1 (2) - (- 3 x)$ .

$\frac{- 1 (2 - 3 x)}{12 x}$

Step 8

Move the negative in front of the fraction.

$- \frac{2 - 3 x}{12 x}$