Precalculus Examples

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

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

Step 1

Dividing two negative values results in a positive value.

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

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

Step 2

To write

\frac{3}{2 y}

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

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

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

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

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

Step 3

To write

- \frac{2}{y + 2}

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

\frac{2 y}{2 y}

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

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

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

Step 4

Write each expression with a common denominator of

2 y (y + 2)

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

1

$1$ .

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Step 4.1

Multiply

\frac{3}{2 y}

$\frac{3}{2 y}$ by

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

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

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

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

Step 4.2

Multiply

\frac{2}{y + 2}

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

\frac{2 y}{2 y}

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

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

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

Step 4.3

Reorder the factors of

(y + 2) (2 y)

$(y + 2) (2 y)$ .

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

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

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

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

Step 5

Combine the numerators over the common denominator.

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

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

Step 6

Simplify the numerator.

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Step 6.1

Apply the distributive property.

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

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

Step 6.2

Multiply

3

$3$ by

2

$2$ .

\frac{3 y + 6 - 2 \cdot 2 y}{2 y (y + 2)}

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

Step 6.3

Multiply

- 2

$- 2$ by

2

$2$ .

\frac{3 y + 6 - 4 y}{2 y (y + 2)}

$\frac{3 y + 6 - 4 y}{2 y (y + 2)}$

Step 6.4

Subtract

4 y

$4 y$ from

3 y

$3 y$ .

\frac{- y + 6}{2 y (y + 2)}

$\frac{- y + 6}{2 y (y + 2)}$

\frac{- y + 6}{2 y (y + 2)}

$\frac{- y + 6}{2 y (y + 2)}$

Step 7

Simplify with factoring out.

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Step 7.1

Factor

- 1

$- 1$ out of

- y

$- y$ .

\frac{- (y) + 6}{2 y (y + 2)}

$\frac{- (y) + 6}{2 y (y + 2)}$

Step 7.2

Rewrite

6

$6$ as

- 1 (- 6)

$- 1 (- 6)$ .

\frac{- (y) - 1 (- 6)}{2 y (y + 2)}

$\frac{- (y) - 1 (- 6)}{2 y (y + 2)}$

Step 7.3

Factor

- 1

$- 1$ out of

- (y) - 1 (- 6)

$- (y) - 1 (- 6)$ .

\frac{- (y - 6)}{2 y (y + 2)}

$\frac{- (y - 6)}{2 y (y + 2)}$

Step 7.4

Simplify the expression.

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Step 7.4.1

Rewrite

- (y - 6)

$- (y - 6)$ as

- 1 (y - 6)

$- 1 (y - 6)$ .

\frac{- 1 (y - 6)}{2 y (y + 2)}

$\frac{- 1 (y - 6)}{2 y (y + 2)}$

Step 7.4.2

Move the negative in front of the fraction.

- \frac{y - 6}{2 y (y + 2)}

$- \frac{y - 6}{2 y (y + 2)}$

- \frac{y - 6}{2 y (y + 2)}

$- \frac{y - 6}{2 y (y + 2)}$

- \frac{y - 6}{2 y (y + 2)}

$- \frac{y - 6}{2 y (y + 2)}$

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