Calculus 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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