Examples

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

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

Step 1

Move the negative in front of the fraction.

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

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

Step 2

To write

\frac{2}{3}

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

\frac{x}{x}

$\frac{x}{x}$ .

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

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

Step 3

Multiply

\frac{2}{3}

$\frac{2}{3}$ by

\frac{x}{x}

$\frac{x}{x}$ .

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

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

Step 5

Factor

2

$2$ out of

- 2 + 2 x

$- 2 + 2 x$ .

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Step 5.1

Factor

2

$2$ out of

- 2

$- 2$ .

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

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

Step 5.2

Factor

2

$2$ out of

2 \cdot - 1 + 2 x

$2 \cdot - 1 + 2 x$ .

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

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

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

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

Step 6

Rewrite

- 1

$- 1$ as

- 1 (1)

$- 1 (1)$ .

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

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

Step 7

Factor

- 1

$- 1$ out of

x

$x$ .

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

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

Step 8

Factor

- 1

$- 1$ out of

- 1 (1) - 1 (- x)

$- 1 (1) - 1 (- x)$ .

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

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

Step 9

Move the negative in front of the fraction.

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

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

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