Solve 1/x-1/2y-2/x-2/3y

$$\frac{ 1 }{ x } - \frac{ 1 }{ 2y } - \frac{ 2 }{ x } - \frac{ 2 }{ 3y }$$

Evaluate

$$\frac{-7x-6y}{6xy}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x and 2y is 2xy. Multiply \frac{1}{x} times \frac{2y}{2y}. Multiply \frac{1}{2y} times \frac{x}{x}.

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

Since \frac{2y}{2xy} and \frac{x}{2xy} have the same denominator, subtract them by subtracting their numerators.

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

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

$$\frac{2y-x}{2xy}-\frac{2\times 2y}{2xy}-\frac{2}{3y}$$

Since \frac{2y-x}{2xy} and \frac{2\times 2y}{2xy} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2y-x-2\times 2y}{2xy}-\frac{2}{3y}$$

Do the multiplications in 2y-x-2\times 2y.

$$\frac{2y-x-4y}{2xy}-\frac{2}{3y}$$

Combine like terms in 2y-x-4y.

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

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

$$\frac{3\left(-2y-x\right)}{6xy}-\frac{2\times 2x}{6xy}$$

Since \frac{3\left(-2y-x\right)}{6xy} and \frac{2\times 2x}{6xy} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3\left(-2y-x\right)-2\times 2x}{6xy}$$

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

$$\frac{-6y-3x-4x}{6xy}$$

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

$$\frac{-6y-7x}{6xy}$$

Factor

$$\frac{-\frac{7x}{y}-6}{6x}$$