Precalculus Examples

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

Step 1

Move the negative in front of the fraction.

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

Step 2

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

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

Step 3

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

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

Step 4

Write each expression with a common denominator of $(y + 2) \cdot 3$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

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

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

Step 4.2

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

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

Step 4.3

Reorder the factors of $(y + 2) \cdot 3$ .

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

Step 5

Combine the numerators over the common denominator.

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

Step 6

Simplify the numerator.

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Step 6.1

Factor $2$ out of $- 2 \cdot 3 + 2 (y + 2)$ .

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Step 6.1.1

Factor $2$ out of $- 2 \cdot 3$ .

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

Step 6.1.2

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

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

Step 6.2

Multiply $- 1$ by $3$ .

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

Step 6.3

Add $- 3$ and $2$ .

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

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