Precalculus Examples

$\frac{- 2}{y + 2} - \frac{3}{4 y}$

Step 1

Move the negative in front of the fraction.

$- \frac{2}{y + 2} - \frac{3}{4 y}$

Step 2

To write $- \frac{2}{y + 2}$ as a fraction with a common denominator, multiply by $\frac{4 y}{4 y}$ .

$- \frac{2}{y + 2} \cdot \frac{4 y}{4 y} - \frac{3}{4 y}$

Step 3

To write $- \frac{3}{4 y}$ as a fraction with a common denominator, multiply by $\frac{y + 2}{y + 2}$ .

$- \frac{2}{y + 2} \cdot \frac{4 y}{4 y} - \frac{3}{4 y} \cdot \frac{y + 2}{y + 2}$

Step 4

Write each expression with a common denominator of $(y + 2) \cdot 4 y$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{2}{y + 2}$ by $\frac{4 y}{4 y}$ .

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

Step 4.2

Multiply $\frac{3}{4 y}$ by $\frac{y + 2}{y + 2}$ .

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

Step 4.3

Reorder the factors of $(y + 2) (4 y)$ .

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

Step 5

Combine the numerators over the common denominator.

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

Step 6

Simplify the numerator.

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Step 6.1

Multiply $- 2$ by $4$ .

$\frac{- 8 y - 3 (y + 2)}{4 y (y + 2)}$

Step 6.2

Apply the distributive property.

$\frac{- 8 y - 3 y - 3 \cdot 2}{4 y (y + 2)}$

Step 6.3

Multiply $- 3$ by $2$ .

$\frac{- 8 y - 3 y - 6}{4 y (y + 2)}$

Step 6.4

Subtract $3 y$ from $- 8 y$ .

$\frac{- 11 y - 6}{4 y (y + 2)}$

Step 7

Simplify with factoring out.

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Step 7.1

Factor $- 1$ out of $- 11 y$ .

$\frac{- (11 y) - 6}{4 y (y + 2)}$

Step 7.2

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

$\frac{- (11 y) - 1 (6)}{4 y (y + 2)}$

Step 7.3

Factor $- 1$ out of $- (11 y) - 1 (6)$ .

$\frac{- (11 y + 6)}{4 y (y + 2)}$

Step 7.4

Simplify the expression.

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Step 7.4.1

Rewrite $- (11 y + 6)$ as $- 1 (11 y + 6)$ .

$\frac{- 1 (11 y + 6)}{4 y (y + 2)}$

Step 7.4.2

Move the negative in front of the fraction.

$- \frac{11 y + 6}{4 y (y + 2)}$

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