Solve 2(1/y-1/x)/frac{1{y}-1/x}

$$\frac { 2 ( \frac { 1 } { y } - \frac { 1 } { x } ) } { \frac { 1 } { y } - \frac { 1 } { x } }$$

Evaluate

$$2$$

Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y and x is xy. Multiply \frac{1}{y} times \frac{x}{x}. Multiply \frac{1}{x} times \frac{y}{y}.

$$\frac{2\left(\frac{x}{xy}-\frac{y}{xy}\right)}{\frac{1}{y}-\frac{1}{x}}$$

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

$$\frac{2\times \frac{x-y}{xy}}{\frac{1}{y}-\frac{1}{x}}$$

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

$$\frac{\frac{2\left(x-y\right)}{xy}}{\frac{1}{y}-\frac{1}{x}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y and x is xy. Multiply \frac{1}{y} times \frac{x}{x}. Multiply \frac{1}{x} times \frac{y}{y}.

$$\frac{\frac{2\left(x-y\right)}{xy}}{\frac{x}{xy}-\frac{y}{xy}}$$

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

$$\frac{\frac{2\left(x-y\right)}{xy}}{\frac{x-y}{xy}}$$

Divide \frac{2\left(x-y\right)}{xy} by \frac{x-y}{xy} by multiplying \frac{2\left(x-y\right)}{xy} by the reciprocal of \frac{x-y}{xy}.

$$\frac{2\left(x-y\right)xy}{xy\left(x-y\right)}$$

Cancel out xy\left(x-y\right) in both numerator and denominator.

$$2$$

Factor

$$2$$