Simplify (x-y)/12+(2x+y)/15+(y-4x)/30

$\frac{x - y}{12} + \frac{2 x + y}{15} + \frac{y - 4 x}{30}$

Step 1

To write $\frac{x - y}{12}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{x - y}{12} \cdot \frac{5}{5} + \frac{2 x + y}{15} + \frac{y - 4 x}{30}$

Step 2

To write $\frac{2 x + y}{15}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{x - y}{12} \cdot \frac{5}{5} + \frac{2 x + y}{15} \cdot \frac{4}{4} + \frac{y - 4 x}{30}$

Step 3

Write each expression with a common denominator of $60$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{x - y}{12}$ by $\frac{5}{5}$ .

$\frac{(x - y) \cdot 5}{12 \cdot 5} + \frac{2 x + y}{15} \cdot \frac{4}{4} + \frac{y - 4 x}{30}$

Multiply $12$ by $5$ .

$\frac{(x - y) \cdot 5}{60} + \frac{2 x + y}{15} \cdot \frac{4}{4} + \frac{y - 4 x}{30}$

Multiply $\frac{2 x + y}{15}$ by $\frac{4}{4}$ .

$\frac{(x - y) \cdot 5}{60} + \frac{(2 x + y) \cdot 4}{15 \cdot 4} + \frac{y - 4 x}{30}$

Multiply $15$ by $4$ .

$\frac{(x - y) \cdot 5}{60} + \frac{(2 x + y) \cdot 4}{60} + \frac{y - 4 x}{30}$

Step 4

Combine the numerators over the common denominator.

$\frac{(x - y) \cdot 5 + (2 x + y) \cdot 4}{60} + \frac{y - 4 x}{30}$

Step 5

Simplify the numerator.

Apply the distributive property.

$\frac{x \cdot 5 - y \cdot 5 + (2 x + y) \cdot 4}{60} + \frac{y - 4 x}{30}$

Move $5$ to the left of $x$ .

$\frac{5 \cdot x - y \cdot 5 + (2 x + y) \cdot 4}{60} + \frac{y - 4 x}{30}$

Multiply $5$ by $- 1$ .

$\frac{5 \cdot x - 5 y + (2 x + y) \cdot 4}{60} + \frac{y - 4 x}{30}$

Apply the distributive property.

$\frac{5 x - 5 y + 2 x \cdot 4 + y \cdot 4}{60} + \frac{y - 4 x}{30}$

Multiply $4$ by $2$ .

$\frac{5 x - 5 y + 8 x + y \cdot 4}{60} + \frac{y - 4 x}{30}$

Move $4$ to the left of $y$ .

$\frac{5 x - 5 y + 8 x + 4 \cdot y}{60} + \frac{y - 4 x}{30}$

Add $5 x$ and $8 x$ .

$\frac{13 x - 5 y + 4 y}{60} + \frac{y - 4 x}{30}$

Add $- 5 y$ and $4 y$ .

$\frac{13 x - y}{60} + \frac{y - 4 x}{30}$

Step 6

To write $\frac{y - 4 x}{30}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{13 x - y}{60} + \frac{y - 4 x}{30} \cdot \frac{2}{2}$

Step 7

Write each expression with a common denominator of $60$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{y - 4 x}{30}$ by $\frac{2}{2}$ .

$\frac{13 x - y}{60} + \frac{(y - 4 x) \cdot 2}{30 \cdot 2}$

Multiply $30$ by $2$ .

$\frac{13 x - y}{60} + \frac{(y - 4 x) \cdot 2}{60}$

Step 8

Combine the numerators over the common denominator.

$\frac{13 x - y + (y - 4 x) \cdot 2}{60}$

Step 9

Simplify the numerator.

Apply the distributive property.

$\frac{13 x - y + y \cdot 2 - 4 x \cdot 2}{60}$

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

$\frac{13 x - y + 2 \cdot y - 4 x \cdot 2}{60}$

Multiply $2$ by $- 4$ .

$\frac{13 x - y + 2 \cdot y - 8 x}{60}$

Subtract $8 x$ from $13 x$ .

$\frac{5 x - y + 2 y}{60}$

Add $- y$ and $2 y$ .

$\frac{5 x + y}{60}$

Simplify (x-y)/12+(2x+y)/15+(y-4x)/30

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