Solve x-y/12+2x+y/15+y-4x/20

$$\frac { x - y } { 12 } + \frac { 2 x + y } { 15 } + \frac { y - 4 x } { 20 }$$

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 12 and 15 is 60. Multiply \frac{x-y}{12} times \frac{5}{5}. Multiply \frac{2x+y}{15} times \frac{4}{4}.

$$\frac{5\left(x-y\right)}{60}+\frac{4\left(2x+y\right)}{60}+\frac{y-4x}{20}$$

Since \frac{5\left(x-y\right)}{60} and \frac{4\left(2x+y\right)}{60} have the same denominator, add them by adding their numerators.

$$\frac{5\left(x-y\right)+4\left(2x+y\right)}{60}+\frac{y-4x}{20}$$

Do the multiplications in 5\left(x-y\right)+4\left(2x+y\right).

$$\frac{5x-5y+8x+4y}{60}+\frac{y-4x}{20}$$

Combine like terms in 5x-5y+8x+4y.

$$\frac{13x-y}{60}+\frac{y-4x}{20}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 60 and 20 is 60. Multiply \frac{y-4x}{20} times \frac{3}{3}.

$$\frac{13x-y}{60}+\frac{3\left(y-4x\right)}{60}$$

Since \frac{13x-y}{60} and \frac{3\left(y-4x\right)}{60} have the same denominator, add them by adding their numerators.

$$\frac{13x-y+3\left(y-4x\right)}{60}$$

Do the multiplications in 13x-y+3\left(y-4x\right).

$$\frac{13x-y+3y-12x}{60}$$

Combine like terms in 13x-y+3y-12x.

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

Expand

$$\frac{x}{60}+\frac{y}{30}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 12 and 15 is 60. Multiply \frac{x-y}{12} times \frac{5}{5}. Multiply \frac{2x+y}{15} times \frac{4}{4}.

$$\frac{5\left(x-y\right)}{60}+\frac{4\left(2x+y\right)}{60}+\frac{y-4x}{20}$$

Since \frac{5\left(x-y\right)}{60} and \frac{4\left(2x+y\right)}{60} have the same denominator, add them by adding their numerators.

$$\frac{5\left(x-y\right)+4\left(2x+y\right)}{60}+\frac{y-4x}{20}$$

Do the multiplications in 5\left(x-y\right)+4\left(2x+y\right).

$$\frac{5x-5y+8x+4y}{60}+\frac{y-4x}{20}$$

Combine like terms in 5x-5y+8x+4y.

$$\frac{13x-y}{60}+\frac{y-4x}{20}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 60 and 20 is 60. Multiply \frac{y-4x}{20} times \frac{3}{3}.

$$\frac{13x-y}{60}+\frac{3\left(y-4x\right)}{60}$$

Since \frac{13x-y}{60} and \frac{3\left(y-4x\right)}{60} have the same denominator, add them by adding their numerators.

$$\frac{13x-y+3\left(y-4x\right)}{60}$$

Do the multiplications in 13x-y+3\left(y-4x\right).

$$\frac{13x-y+3y-12x}{60}$$

Combine like terms in 13x-y+3y-12x.

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