Solve xy(x+y)(1/x-1/y)

$$x y ( x + y ) ( \frac { 1 } { x } - \frac { 1 } { y } )$$

Evaluate

$$y^{2}-x^{2}$$

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}.

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

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

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

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

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

Cancel out x in both numerator and denominator.

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

Cancel out y and y.

$$\left(-x+y\right)\left(x+y\right)$$

Apply the distributive property by multiplying each term of -x+y by each term of x+y.

$$-x^{2}-xy+yx+y^{2}$$

Combine -xy and yx to get 0.

$$-x^{2}+y^{2}$$

Expand

$$y^{2}-x^{2}$$

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}.

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

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

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

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

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

Cancel out x in both numerator and denominator.

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

Cancel out y and y.

$$\left(-x+y\right)\left(x+y\right)$$

Apply the distributive property by multiplying each term of -x+y by each term of x+y.

$$-x^{2}-xy+yx+y^{2}$$

Combine -xy and yx to get 0.

$$-x^{2}+y^{2}$$