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

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

Evaluate

$$-\frac{x}{6y}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3y and 2y is 6y. Multiply \frac{x}{3y} times \frac{2}{2}. Multiply \frac{x}{2y} times \frac{3}{3}.

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

Since \frac{2x}{6y} and \frac{3x}{6y} have the same denominator, add them by adding their numerators.

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

Combine like terms in 2x+3x.

$$\frac{5x}{6y}-\frac{x}{y}$$

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

$$\frac{5x}{6y}-\frac{6x}{6y}$$

Since \frac{5x}{6y} and \frac{6x}{6y} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5x-6x}{6y}$$

Combine like terms in 5x-6x.

$$\frac{-x}{6y}$$

Cancel out -1 in both numerator and denominator.

$$\frac{x}{-6y}$$

Differentiate w.r.t. x

$$-\frac{1}{6y}$$