Solve (3x-2y/4-x+3y/8)+(x+y/3+2x+y/6)

$$( \frac { 3 x - 2 y } { 4 } - \frac { x + 3 y } { 8 } ) + ( \frac { x + y } { 3 } + \frac { 2 x + y } { 6 } )$$

Evaluate

$$\frac{31x}{24}-\frac{3y}{8}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 8 is 8. Multiply \frac{3x-2y}{4} times \frac{2}{2}.

$$\frac{2\left(3x-2y\right)}{8}-\frac{x+3y}{8}+\frac{x+y}{3}+\frac{2x+y}{6}$$

Since \frac{2\left(3x-2y\right)}{8} and \frac{x+3y}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\left(3x-2y\right)-\left(x+3y\right)}{8}+\frac{x+y}{3}+\frac{2x+y}{6}$$

Do the multiplications in 2\left(3x-2y\right)-\left(x+3y\right).

$$\frac{6x-4y-x-3y}{8}+\frac{x+y}{3}+\frac{2x+y}{6}$$

Combine like terms in 6x-4y-x-3y.

$$\frac{5x-7y}{8}+\frac{x+y}{3}+\frac{2x+y}{6}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 8 and 3 is 24. Multiply \frac{5x-7y}{8} times \frac{3}{3}. Multiply \frac{x+y}{3} times \frac{8}{8}.

$$\frac{3\left(5x-7y\right)}{24}+\frac{8\left(x+y\right)}{24}+\frac{2x+y}{6}$$

Since \frac{3\left(5x-7y\right)}{24} and \frac{8\left(x+y\right)}{24} have the same denominator, add them by adding their numerators.

$$\frac{3\left(5x-7y\right)+8\left(x+y\right)}{24}+\frac{2x+y}{6}$$

Do the multiplications in 3\left(5x-7y\right)+8\left(x+y\right).

$$\frac{15x-21y+8x+8y}{24}+\frac{2x+y}{6}$$

Combine like terms in 15x-21y+8x+8y.

$$\frac{23x-13y}{24}+\frac{2x+y}{6}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 24 and 6 is 24. Multiply \frac{2x+y}{6} times \frac{4}{4}.

$$\frac{23x-13y}{24}+\frac{4\left(2x+y\right)}{24}$$

Since \frac{23x-13y}{24} and \frac{4\left(2x+y\right)}{24} have the same denominator, add them by adding their numerators.

$$\frac{23x-13y+4\left(2x+y\right)}{24}$$

Do the multiplications in 23x-13y+4\left(2x+y\right).

$$\frac{23x-13y+8x+4y}{24}$$

Combine like terms in 23x-13y+8x+4y.

$$\frac{31x-9y}{24}$$

Expand

$$\frac{31x}{24}-\frac{3y}{8}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 8 is 8. Multiply \frac{3x-2y}{4} times \frac{2}{2}.

$$\frac{2\left(3x-2y\right)}{8}-\frac{x+3y}{8}+\frac{x+y}{3}+\frac{2x+y}{6}$$

Since \frac{2\left(3x-2y\right)}{8} and \frac{x+3y}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\left(3x-2y\right)-\left(x+3y\right)}{8}+\frac{x+y}{3}+\frac{2x+y}{6}$$

Do the multiplications in 2\left(3x-2y\right)-\left(x+3y\right).

$$\frac{6x-4y-x-3y}{8}+\frac{x+y}{3}+\frac{2x+y}{6}$$

Combine like terms in 6x-4y-x-3y.

$$\frac{5x-7y}{8}+\frac{x+y}{3}+\frac{2x+y}{6}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 8 and 3 is 24. Multiply \frac{5x-7y}{8} times \frac{3}{3}. Multiply \frac{x+y}{3} times \frac{8}{8}.

$$\frac{3\left(5x-7y\right)}{24}+\frac{8\left(x+y\right)}{24}+\frac{2x+y}{6}$$

Since \frac{3\left(5x-7y\right)}{24} and \frac{8\left(x+y\right)}{24} have the same denominator, add them by adding their numerators.

$$\frac{3\left(5x-7y\right)+8\left(x+y\right)}{24}+\frac{2x+y}{6}$$

Do the multiplications in 3\left(5x-7y\right)+8\left(x+y\right).

$$\frac{15x-21y+8x+8y}{24}+\frac{2x+y}{6}$$

Combine like terms in 15x-21y+8x+8y.

$$\frac{23x-13y}{24}+\frac{2x+y}{6}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 24 and 6 is 24. Multiply \frac{2x+y}{6} times \frac{4}{4}.

$$\frac{23x-13y}{24}+\frac{4\left(2x+y\right)}{24}$$

Since \frac{23x-13y}{24} and \frac{4\left(2x+y\right)}{24} have the same denominator, add them by adding their numerators.

$$\frac{23x-13y+4\left(2x+y\right)}{24}$$

Do the multiplications in 23x-13y+4\left(2x+y\right).

$$\frac{23x-13y+8x+4y}{24}$$

Combine like terms in 23x-13y+8x+4y.

$$\frac{31x-9y}{24}$$