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

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

Evaluate

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

Short Solution Steps

Factor the expressions that are not already factored.

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

Cancel out \frac{1}{x} in both numerator and denominator.

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

Express \frac{1}{y}x as a single fraction.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{y}{y}.

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

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

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

Express \frac{1}{y}x as a single fraction.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{y}{y}.

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

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

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

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

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

Cancel out y in both numerator and denominator.

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

Expand

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

Short Solution Steps

Factor the expressions that are not already factored.

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

Cancel out \frac{1}{x} in both numerator and denominator.

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

Express \frac{1}{y}x as a single fraction.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{y}{y}.

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

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

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

Express \frac{1}{y}x as a single fraction.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{y}{y}.

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

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

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

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

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

Cancel out y in both numerator and denominator.

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