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

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

Evaluate

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

Short Solution Steps

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

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

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

$$\frac{1}{x-y}\times \frac{xx-yy}{xy}$$

Do the multiplications in xx-yy.

$$\frac{1}{x-y}\times \frac{x^{2}-y^{2}}{xy}$$

Multiply \frac{1}{x-y} times \frac{x^{2}-y^{2}}{xy} by multiplying numerator times numerator and denominator times denominator.

$$\frac{x^{2}-y^{2}}{\left(x-y\right)xy}$$

Factor the expressions that are not already factored.

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

Cancel out x-y in both numerator and denominator.

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

Expand

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

Short Solution Steps

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

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

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

$$\frac{1}{x-y}\times \frac{xx-yy}{xy}$$

Do the multiplications in xx-yy.

$$\frac{1}{x-y}\times \frac{x^{2}-y^{2}}{xy}$$

Multiply \frac{1}{x-y} times \frac{x^{2}-y^{2}}{xy} by multiplying numerator times numerator and denominator times denominator.

$$\frac{x^{2}-y^{2}}{\left(x-y\right)xy}$$

Factor the expressions that are not already factored.

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

Cancel out x-y in both numerator and denominator.

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