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

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

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\left(x+y\right) and x\left(x+y\right) is xy\left(x+y\right). Multiply \frac{x}{y\left(x+y\right)} times \frac{x}{x}. Multiply \frac{y}{x\left(x+y\right)} times \frac{y}{y}.

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

Since \frac{xx}{xy\left(x+y\right)} and \frac{yy}{xy\left(x+y\right)} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in xx-yy.

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

Factor the expressions that are not already factored in \frac{x^{2}-y^{2}}{xy\left(x+y\right)}.

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

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\left(x+y\right) and x\left(x+y\right) is xy\left(x+y\right). Multiply \frac{x}{y\left(x+y\right)} times \frac{x}{x}. Multiply \frac{y}{x\left(x+y\right)} times \frac{y}{y}.

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

Since \frac{xx}{xy\left(x+y\right)} and \frac{yy}{xy\left(x+y\right)} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in xx-yy.

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

Factor the expressions that are not already factored in \frac{x^{2}-y^{2}}{xy\left(x+y\right)}.

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

Cancel out x+y in both numerator and denominator.

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