Solve x/x-x/y/frac{2{x}-2/y}

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

Evaluate

$$\frac{x}{2}$$

Short Solution Steps

Divide x by x to get 1.

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

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

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

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

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x and y is xy. Multiply \frac{2}{x} times \frac{y}{y}. Multiply \frac{2}{y} times \frac{x}{x}.

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

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

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

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

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

Cancel out y in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out -x+y in both numerator and denominator.

$$\frac{x}{2}$$

Expand

$$\frac{x}{2}$$

Short Solution Steps

Divide x by x to get 1.

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

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

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

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

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x and y is xy. Multiply \frac{2}{x} times \frac{y}{y}. Multiply \frac{2}{y} times \frac{x}{x}.

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

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

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

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

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

Cancel out y in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out -x+y in both numerator and denominator.

$$\frac{x}{2}$$