Precalculus Examples

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

Step 1

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

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

Step 2

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

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

Step 3

Write each expression with a common denominator of $6 y$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

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

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

Step 3.2

Multiply $3$ by $2$ .

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

Step 3.3

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

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

Step 3.4

Multiply $2$ by $3$ .

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Simplify the numerator.

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Step 5.1

Multiply $- 3$ by $3$ .

$\frac{- 9 y + 2 \cdot 2}{6 y}$

Step 5.2

Multiply $2$ by $2$ .

$\frac{- 9 y + 4}{6 y}$

Step 6

Simplify with factoring out.

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Step 6.1

Factor $- 1$ out of $- 9 y$ .

$\frac{- (9 y) + 4}{6 y}$

Step 6.2

Rewrite $4$ as $- 1 (- 4)$ .

$\frac{- (9 y) - 1 (- 4)}{6 y}$

Step 6.3

Factor $- 1$ out of $- (9 y) - 1 (- 4)$ .

$\frac{- (9 y - 4)}{6 y}$

Step 6.4

Simplify the expression.

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Step 6.4.1

Rewrite $- (9 y - 4)$ as $- 1 (9 y - 4)$ .

$\frac{- 1 (9 y - 4)}{6 y}$

Step 6.4.2

Move the negative in front of the fraction.

$- \frac{9 y - 4}{6 y}$

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