Solve 1/x-1/y/x-y

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

Evaluate

$$-\frac{1}{xy}$$

Solution Steps

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

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

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

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

Express \frac{\frac{y-x}{xy}}{x-y} as a single fraction.

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

Extract the negative sign in y-x.

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

Cancel out x-y in both numerator and denominator.

$$\frac{-1}{xy}$$

Expand

$$-\frac{1}{xy}$$

Solution Steps

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

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

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

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

Express \frac{\frac{y-x}{xy}}{x-y} as a single fraction.

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

Extract the negative sign in y-x.

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

Cancel out x-y in both numerator and denominator.

$$\frac{-1}{xy}$$