Solve (y/x+x/y-2)+(y/x-x/y)

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

Evaluate

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

Short Solution Steps

Combine \frac{y}{x} and \frac{y}{x} to get 2\times \frac{y}{x}.

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

Subtract \frac{x}{y} from \frac{x}{y} to get 0.

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

Express 2\times \frac{y}{x} as a single fraction.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{x}{x}.

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

Since \frac{2y}{x} and \frac{2x}{x} have the same denominator, subtract them by subtracting their numerators.

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

Differentiate w.r.t. x

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