Examples

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

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

Step 1

Move the negative in front of the fraction.

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

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

Step 2

To write

- \frac{2}{y + 2}

$- \frac{2}{y + 2}$ as a fraction with a common denominator, multiply by

\frac{3}{3}

$\frac{3}{3}$ .

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

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

Step 3

To write

\frac{2}{3}

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

\frac{y + 2}{y + 2}

$\frac{y + 2}{y + 2}$ .

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

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

Step 4

Write each expression with a common denominator of

(y + 2) \cdot 3

$(y + 2) \cdot 3$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 4.1

Multiply

\frac{2}{y + 2}

$\frac{2}{y + 2}$ by

\frac{3}{3}

$\frac{3}{3}$ .

- \frac{2 \cdot 3}{(y + 2) \cdot 3} + \frac{2}{3} \cdot \frac{y + 2}{y + 2}

$- \frac{2 \cdot 3}{(y + 2) \cdot 3} + \frac{2}{3} \cdot \frac{y + 2}{y + 2}$

Step 4.2

Multiply

\frac{2}{3}

$\frac{2}{3}$ by

\frac{y + 2}{y + 2}

$\frac{y + 2}{y + 2}$ .

- \frac{2 \cdot 3}{(y + 2) \cdot 3} + \frac{2 (y + 2)}{3 (y + 2)}

$- \frac{2 \cdot 3}{(y + 2) \cdot 3} + \frac{2 (y + 2)}{3 (y + 2)}$

Step 4.3

Reorder the factors of

(y + 2) \cdot 3

$(y + 2) \cdot 3$ .

- \frac{2 \cdot 3}{3 (y + 2)} + \frac{2 (y + 2)}{3 (y + 2)}

$- \frac{2 \cdot 3}{3 (y + 2)} + \frac{2 (y + 2)}{3 (y + 2)}$

- \frac{2 \cdot 3}{3 (y + 2)} + \frac{2 (y + 2)}{3 (y + 2)}

$- \frac{2 \cdot 3}{3 (y + 2)} + \frac{2 (y + 2)}{3 (y + 2)}$

Step 5

Combine the numerators over the common denominator.

\frac{- 2 \cdot 3 + 2 (y + 2)}{3 (y + 2)}

$\frac{- 2 \cdot 3 + 2 (y + 2)}{3 (y + 2)}$

Step 6

Simplify the numerator.

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Step 6.1

Factor

2

$2$ out of

- 2 \cdot 3 + 2 (y + 2)

$- 2 \cdot 3 + 2 (y + 2)$ .

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Step 6.1.1

Factor

2

$2$ out of

- 2 \cdot 3

$- 2 \cdot 3$ .

\frac{2 (- 1 \cdot 3) + 2 (y + 2)}{3 (y + 2)}

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

Step 6.1.2

Factor

2

$2$ out of

2 (- 1 \cdot 3) + 2 (y + 2)

$2 (- 1 \cdot 3) + 2 (y + 2)$ .

\frac{2 (- 1 \cdot 3 + y + 2)}{3 (y + 2)}

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

\frac{2 (- 1 \cdot 3 + y + 2)}{3 (y + 2)}

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

Step 6.2

Multiply

- 1

$- 1$ by

3

$3$ .

\frac{2 (- 3 + y + 2)}{3 (y + 2)}

$\frac{2 (- 3 + y + 2)}{3 (y + 2)}$

Step 6.3

Add

- 3

$- 3$ and

2

$2$ .

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

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

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

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

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