Solve x^-1+y^-1/(xy)^-1=

$$\frac { x ^ { - 1 } + y ^ { - 1 } } { ( x y ) ^ { - 1 } } =$$

Evaluate

$$x+y$$

Short Solution Steps

Expand \left(xy\right)^{-1}.

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

Factor the expressions that are not already factored.

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

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

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

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

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

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

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

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

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

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

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

Cancel out y in both numerator and denominator.

$$x+y$$

Expand

$$x+y$$

Short Solution Steps

Expand \left(xy\right)^{-1}.

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

Factor the expressions that are not already factored.

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

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

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

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

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

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

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

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

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

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

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

Cancel out y in both numerator and denominator.

$$x+y$$