Simplify y/6-(3x)/4+(3y)/2

$\frac{y}{6} - \frac{3 x}{4} + \frac{3 y}{2}$

Step 1

To write $\frac{y}{6}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 2

To write $- \frac{3 x}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 3

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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

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

Multiply $6$ by $2$ .

$\frac{y \cdot 2}{12} - \frac{3 x}{4} \cdot \frac{3}{3} + \frac{3 y}{2}$

Multiply $\frac{3 x}{4}$ by $\frac{3}{3}$ .

$\frac{y \cdot 2}{12} - \frac{3 x \cdot 3}{4 \cdot 3} + \frac{3 y}{2}$

Multiply $4$ by $3$ .

$\frac{y \cdot 2}{12} - \frac{3 x \cdot 3}{12} + \frac{3 y}{2}$

Step 4

Combine the numerators over the common denominator.

$\frac{y \cdot 2 - 3 x \cdot 3}{12} + \frac{3 y}{2}$

Step 5

Simplify the numerator.

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

$\frac{2 \cdot y - 3 x \cdot 3}{12} + \frac{3 y}{2}$

Multiply $3$ by $- 3$ .

$\frac{2 y - 9 x}{12} + \frac{3 y}{2}$

Step 6

To write $\frac{3 y}{2}$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{2 y - 9 x}{12} + \frac{3 y}{2} \cdot \frac{6}{6}$

Step 7

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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

$\frac{2 y - 9 x}{12} + \frac{3 y \cdot 6}{2 \cdot 6}$

Multiply $2$ by $6$ .

$\frac{2 y - 9 x}{12} + \frac{3 y \cdot 6}{12}$

Step 8

Combine the numerators over the common denominator.

$\frac{2 y - 9 x + 3 y \cdot 6}{12}$

Step 9

Simplify the numerator.

Multiply $6$ by $3$ .

$\frac{2 y - 9 x + 18 y}{12}$

Add $2 y$ and $18 y$ .

$\frac{- 9 x + 20 y}{12}$

Step 10

Simplify with factoring out.

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

$\frac{- (9 x) + 20 y}{12}$

Factor $- 1$ out of $20 y$ .

$\frac{- (9 x) - (- 20 y)}{12}$

Factor $- 1$ out of $- (9 x) - (- 20 y)$ .

$\frac{- (9 x - 20 y)}{12}$

Simplify the expression.

Rewrite $- (9 x - 20 y)$ as $- 1 (9 x - 20 y)$ .

$\frac{- 1 (9 x - 20 y)}{12}$

Move the negative in front of the fraction.

$- \frac{9 x - 20 y}{12}$

Simplify y/6-(3x)/4+(3y)/2

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