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

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

Evaluate

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

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}.

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

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

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

Multiply \frac{x}{x-y} times \frac{y-x}{xy} by multiplying numerator times numerator and denominator times denominator.

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

Extract the negative sign in y-x.

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

Cancel out x\left(x-y\right) in both numerator and denominator.

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

Expand

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

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}.

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

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

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

Multiply \frac{x}{x-y} times \frac{y-x}{xy} by multiplying numerator times numerator and denominator times denominator.

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

Extract the negative sign in y-x.

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

Cancel out x\left(x-y\right) in both numerator and denominator.

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