Solve 5x-2y/4-4x+3y/3+2x+5y/2

$$\frac { 5 x - 2 y } { 4 } - \frac { 4 x + 3 y } { 3 } + \frac { 2 x + 5 y } { 2 }$$

Evaluate

$$\frac{11x}{12}+y$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 3 is 12. Multiply \frac{5x-2y}{4} times \frac{3}{3}. Multiply \frac{4x+3y}{3} times \frac{4}{4}.

$$\frac{3\left(5x-2y\right)}{12}-\frac{4\left(4x+3y\right)}{12}+\frac{2x+5y}{2}$$

Since \frac{3\left(5x-2y\right)}{12} and \frac{4\left(4x+3y\right)}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3\left(5x-2y\right)-4\left(4x+3y\right)}{12}+\frac{2x+5y}{2}$$

Do the multiplications in 3\left(5x-2y\right)-4\left(4x+3y\right).

$$\frac{15x-6y-16x-12y}{12}+\frac{2x+5y}{2}$$

Combine like terms in 15x-6y-16x-12y.

$$\frac{-x-18y}{12}+\frac{2x+5y}{2}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 12 and 2 is 12. Multiply \frac{2x+5y}{2} times \frac{6}{6}.

$$\frac{-x-18y}{12}+\frac{6\left(2x+5y\right)}{12}$$

Since \frac{-x-18y}{12} and \frac{6\left(2x+5y\right)}{12} have the same denominator, add them by adding their numerators.

$$\frac{-x-18y+6\left(2x+5y\right)}{12}$$

Do the multiplications in -x-18y+6\left(2x+5y\right).

$$\frac{-x-18y+12x+30y}{12}$$

Combine like terms in -x-18y+12x+30y.

$$\frac{11x+12y}{12}$$

Expand

$$\frac{11x}{12}+y$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 3 is 12. Multiply \frac{5x-2y}{4} times \frac{3}{3}. Multiply \frac{4x+3y}{3} times \frac{4}{4}.

$$\frac{3\left(5x-2y\right)}{12}-\frac{4\left(4x+3y\right)}{12}+\frac{2x+5y}{2}$$

Since \frac{3\left(5x-2y\right)}{12} and \frac{4\left(4x+3y\right)}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3\left(5x-2y\right)-4\left(4x+3y\right)}{12}+\frac{2x+5y}{2}$$

Do the multiplications in 3\left(5x-2y\right)-4\left(4x+3y\right).

$$\frac{15x-6y-16x-12y}{12}+\frac{2x+5y}{2}$$

Combine like terms in 15x-6y-16x-12y.

$$\frac{-x-18y}{12}+\frac{2x+5y}{2}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 12 and 2 is 12. Multiply \frac{2x+5y}{2} times \frac{6}{6}.

$$\frac{-x-18y}{12}+\frac{6\left(2x+5y\right)}{12}$$

Since \frac{-x-18y}{12} and \frac{6\left(2x+5y\right)}{12} have the same denominator, add them by adding their numerators.

$$\frac{-x-18y+6\left(2x+5y\right)}{12}$$

Do the multiplications in -x-18y+6\left(2x+5y\right).

$$\frac{-x-18y+12x+30y}{12}$$

Combine like terms in -x-18y+12x+30y.

$$\frac{11x+12y}{12}$$