Examples

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

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

Step 1

To write

- \frac{3}{2}

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

\frac{3 y}{3 y}

$\frac{3 y}{3 y}$ .

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

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

Step 2

To write

\frac{2}{3 y}

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

\frac{2}{2}

$\frac{2}{2}$ .

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

$6 y$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 3.1

Multiply

\frac{3}{2}

$\frac{3}{2}$ by

\frac{3 y}{3 y}

$\frac{3 y}{3 y}$ .

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

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

Step 3.2

Multiply

3

$3$ by

2

$2$ .

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

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

Step 3.3

Multiply

\frac{2}{3 y}

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

\frac{2}{2}

$\frac{2}{2}$ .

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

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

Step 3.4

Multiply

2

$2$ by

3

$3$ .

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

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

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

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

Step 4

Combine the numerators over the common denominator.

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

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

Step 5

Simplify the numerator.

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Step 5.1

Multiply

- 3

$- 3$ by

3

$3$ .

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

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

Step 5.2

Multiply

2

$2$ by

2

$2$ .

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

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

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

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

Step 6

Simplify with factoring out.

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Step 6.1

Factor

- 1

$- 1$ out of

- 9 y

$- 9 y$ .

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

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

Step 6.2

Rewrite

4

$4$ as

- 1 (- 4)

$- 1 (- 4)$ .

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

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

Step 6.3

Factor

- 1

$- 1$ out of

- (9 y) - 1 (- 4)

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

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

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

Step 6.4

Simplify the expression.

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Step 6.4.1

Rewrite

- (9 y - 4)

$- (9 y - 4)$ as

- 1 (9 y - 4)

$- 1 (9 y - 4)$ .

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

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

Step 6.4.2

Move the negative in front of the fraction.

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

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

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

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

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

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

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