Precalculus Examples

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

Step 1

Dividing two negative values results in a positive value.

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

Step 2

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

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

Step 3

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

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

Step 4

Write each expression with a common denominator of $2 y (y + 2)$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{3}{2 y}$ by $\frac{y + 2}{y + 2}$ .

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

Step 4.2

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

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

Step 4.3

Reorder the factors of $(y + 2) (2 y)$ .

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

Step 5

Combine the numerators over the common denominator.

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

Step 6

Simplify the numerator.

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Step 6.1

Apply the distributive property.

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

Step 6.2

Multiply $3$ by $2$ .

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

Step 6.3

Multiply $- 2$ by $2$ .

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

Step 6.4

Subtract $4 y$ from $3 y$ .

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

Step 7

Simplify with factoring out.

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Step 7.1

Factor $- 1$ out of $- y$ .

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

Step 7.2

Rewrite $6$ as $- 1 (- 6)$ .

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

Step 7.3

Factor $- 1$ out of $- (y) - 1 (- 6)$ .

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

Step 7.4

Simplify the expression.

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Step 7.4.1

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

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

Step 7.4.2

Move the negative in front of the fraction.

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

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