Evaluate (8-y)/(3y)+(y+2)/(9y)-2/(6y)

$\frac{8 - y}{3 y} + \frac{y + 2}{9 y} - \frac{2}{6 y}$

Step 1

Find the common denominator.

Multiply $\frac{8 - y}{3 y}$ by $\frac{6}{6}$ .

$\frac{8 - y}{3 y} \cdot \frac{6}{6} + \frac{y + 2}{9 y} - \frac{2}{6 y}$

Multiply $\frac{8 - y}{3 y}$ by $\frac{6}{6}$ .

$\frac{(8 - y) \cdot 6}{3 y \cdot 6} + \frac{y + 2}{9 y} - \frac{2}{6 y}$

Multiply $\frac{y + 2}{9 y}$ by $\frac{2}{2}$ .

$\frac{(8 - y) \cdot 6}{3 y \cdot 6} + \frac{y + 2}{9 y} \cdot \frac{2}{2} - \frac{2}{6 y}$

Multiply $\frac{y + 2}{9 y}$ by $\frac{2}{2}$ .

$\frac{(8 - y) \cdot 6}{3 y \cdot 6} + \frac{(y + 2) \cdot 2}{9 y \cdot 2} - \frac{2}{6 y}$

Multiply $\frac{2}{6 y}$ by $\frac{3}{3}$ .

$\frac{(8 - y) \cdot 6}{3 y \cdot 6} + \frac{(y + 2) \cdot 2}{9 y \cdot 2} - (\frac{2}{6 y} \cdot \frac{3}{3})$

Multiply $\frac{2}{6 y}$ by $\frac{3}{3}$ .

$\frac{(8 - y) \cdot 6}{3 y \cdot 6} + \frac{(y + 2) \cdot 2}{9 y \cdot 2} - \frac{2 \cdot 3}{6 y \cdot 3}$

Reorder the factors of $3 y \cdot 6$ .

$\frac{(8 - y) \cdot 6}{3 \cdot 6 y} + \frac{(y + 2) \cdot 2}{9 y \cdot 2} - \frac{2 \cdot 3}{6 y \cdot 3}$

Multiply $3$ by $6$ .

$\frac{(8 - y) \cdot 6}{18 y} + \frac{(y + 2) \cdot 2}{9 y \cdot 2} - \frac{2 \cdot 3}{6 y \cdot 3}$

Reorder the factors of $9 y \cdot 2$ .

$\frac{(8 - y) \cdot 6}{18 y} + \frac{(y + 2) \cdot 2}{2 \cdot 9 y} - \frac{2 \cdot 3}{6 y \cdot 3}$

Multiply $2$ by $9$ .

$\frac{(8 - y) \cdot 6}{18 y} + \frac{(y + 2) \cdot 2}{18 y} - \frac{2 \cdot 3}{6 y \cdot 3}$

Reorder the factors of $6 y \cdot 3$ .

$\frac{(8 - y) \cdot 6}{18 y} + \frac{(y + 2) \cdot 2}{18 y} - \frac{2 \cdot 3}{3 \cdot 6 y}$

Multiply $3$ by $6$ .

$\frac{(8 - y) \cdot 6}{18 y} + \frac{(y + 2) \cdot 2}{18 y} - \frac{2 \cdot 3}{18 y}$

Step 2

Combine the numerators over the common denominator.

$\frac{(8 - y) \cdot 6 + (y + 2) \cdot 2 - 2 \cdot 3}{18 y}$

Step 3

Simplify each term.

Apply the distributive property.

$\frac{8 \cdot 6 - y \cdot 6 + (y + 2) \cdot 2 - 2 \cdot 3}{18 y}$

Multiply $8$ by $6$ .

$\frac{48 - y \cdot 6 + (y + 2) \cdot 2 - 2 \cdot 3}{18 y}$

Multiply $6$ by $- 1$ .

$\frac{48 - 6 y + (y + 2) \cdot 2 - 2 \cdot 3}{18 y}$

Apply the distributive property.

$\frac{48 - 6 y + y \cdot 2 + 2 \cdot 2 - 2 \cdot 3}{18 y}$

Move $2$ to the left of $y$ .

$\frac{48 - 6 y + 2 \cdot y + 2 \cdot 2 - 2 \cdot 3}{18 y}$

Multiply $2$ by $2$ .

$\frac{48 - 6 y + 2 \cdot y + 4 - 2 \cdot 3}{18 y}$

Multiply $- 2$ by $3$ .

$\frac{48 - 6 y + 2 y + 4 - 6}{18 y}$

Step 4

Simplify terms.

Add $48$ and $4$ .

$\frac{- 6 y + 2 y + 52 - 6}{18 y}$

Add $- 6 y$ and $2 y$ .

$\frac{- 4 y + 52 - 6}{18 y}$

Subtract $6$ from $52$ .

$\frac{- 4 y + 46}{18 y}$

Cancel the common factor of $- 4 y + 46$ and $18$ .

Factor $2$ out of $- 4 y$ .

$\frac{2 (- 2 y) + 46}{18 y}$

Factor $2$ out of $46$ .

$\frac{2 (- 2 y) + 2 (23)}{18 y}$

Factor $2$ out of $2 (- 2 y) + 2 (23)$ .

$\frac{2 (- 2 y + 23)}{18 y}$

Cancel the common factors.

Factor $2$ out of $18 y$ .

$\frac{2 (- 2 y + 23)}{2 (9 y)}$

Cancel the common factor.

$\frac{2 (- 2 y + 23)}{2 (9 y)}$

Rewrite the expression.

$\frac{- 2 y + 23}{9 y}$

Factor $- 1$ out of $- 2 y$ .

$\frac{- (2 y) + 23}{9 y}$

Rewrite $23$ as $- 1 (- 23)$ .

$\frac{- (2 y) - 1 (- 23)}{9 y}$

Factor $- 1$ out of $- (2 y) - 1 (- 23)$ .

$\frac{- (2 y - 23)}{9 y}$

Simplify the expression.

Rewrite $- (2 y - 23)$ as $- 1 (2 y - 23)$ .

$\frac{- 1 (2 y - 23)}{9 y}$

Move the negative in front of the fraction.

$- \frac{2 y - 23}{9 y}$

Evaluate (8-y)/(3y)+(y+2)/(9y)-2/(6y)

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