Solve 3/x(x-y)-3/y(x-y)

$$\frac{ 3 }{ x(x-y) } - \frac{ 3 }{ y(x-y) }$$

Evaluate

$$-\frac{3}{xy}$$

Short Solution Steps

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

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

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

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

Factor the expressions that are not already factored in \frac{3y-3x}{xy\left(x-y\right)}.

$$\frac{3\left(-x+y\right)}{xy\left(x-y\right)}$$

Extract the negative sign in y-x.

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

Cancel out x-y in both numerator and denominator.

$$\frac{-3}{xy}$$

Expand

$$-\frac{3}{xy}$$

Short Solution Steps

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

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

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

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

Factor the expressions that are not already factored in \frac{3y-3x}{xy\left(x-y\right)}.

$$\frac{3\left(-x+y\right)}{xy\left(x-y\right)}$$

Extract the negative sign in y-x.

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

Cancel out x-y in both numerator and denominator.

$$\frac{-3}{xy}$$