Solve 1/x-1/y/frac{1{xy}}

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

Evaluate

$$y-x$$

Solution Steps

Divide \frac{1}{x}-\frac{1}{y} by \frac{1}{xy} by multiplying \frac{1}{x}-\frac{1}{y} by the reciprocal of \frac{1}{xy}.

$$\left(\frac{1}{x}-\frac{1}{y}\right)xy$$

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}.

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

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

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

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

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

Cancel out x in both numerator and denominator.

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

Cancel out y and y.

$$-x+y$$

Expand

$$y-x$$

Solution Steps

Divide \frac{1}{x}-\frac{1}{y} by \frac{1}{xy} by multiplying \frac{1}{x}-\frac{1}{y} by the reciprocal of \frac{1}{xy}.

$$\left(\frac{1}{x}-\frac{1}{y}\right)xy$$

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}.

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

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

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

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

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

Cancel out x in both numerator and denominator.

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

Cancel out y and y.

$$-x+y$$