Precalculus Examples

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

Simplify each term.

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Dividing two negative values results in a positive value.

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

Multiply $2$ by $y$ .

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

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

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

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

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

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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Combine.

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

Combine.

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

Reorder terms.

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

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Apply the distributive property.

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

Multiply $3$ by $2$ .

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

Multiply $2$ by $2$ .

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

Multiply $4$ by $- 1$ .

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

Subtract $4 y$ from $3 y$ .

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

Simplify with factoring out.

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

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

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

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

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

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

Simplify the expression.

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

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

Move the negative in front of the fraction.

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

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