Solve x+y/x^-1y-y^-1x

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

Evaluate

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

Short Solution Steps

Factor the expressions that are not already factored.

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

Extract the negative sign in x+y.

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

Cancel out -x-y in both numerator and denominator.

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

Expand the expression.

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

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}.

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

Since -\frac{y}{xy} and \frac{x}{xy} have the same denominator, add them by adding their numerators.

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

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

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

Expand

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

Short Solution Steps

Factor the expressions that are not already factored.

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

Extract the negative sign in x+y.

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

Cancel out -x-y in both numerator and denominator.

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

Expand the expression.

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

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}.

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

Since -\frac{y}{xy} and \frac{x}{xy} have the same denominator, add them by adding their numerators.

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

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

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