Solve frac{x^{-1}+y^{-1}}{x^-1}+x^-1-y^-1/x^-1=

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

Evaluate

$$2$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{-1}+y^{-1}}{x^{-1}}.

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

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

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

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

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

Factor the expressions that are not already factored in \frac{x^{-1}-y^{-1}}{x^{-1}}.

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

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

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

Add 1 and 1 to get 2.

$$2+\frac{x}{y}-\frac{1}{y}x$$

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

$$2+\frac{x}{y}-\frac{x}{y}$$

Combine \frac{x}{y} and -\frac{x}{y} to get 0.

$$2$$

Factor

$$2$$