Precalculus Examples

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

Step 1

Move the negative in front of the fraction.

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

Step 2

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

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

Step 3

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

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Factor $2$ out of $- 2 + 2 x$ .

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Step 5.1

Factor $2$ out of $- 2$ .

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

Step 5.2

Factor $2$ out of $2 \cdot - 1 + 2 x$ .

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

Step 6

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

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

Step 7

Factor $- 1$ out of $x$ .

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

Step 8

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

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

Step 9

Move the negative in front of the fraction.

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

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