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

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

Evaluate

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

Solution Steps

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

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

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

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

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

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

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

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

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

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

Cancel out y in both numerator and denominator.

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

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

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

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

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

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

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

Cancel out x in both numerator and denominator.

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

Multiply \frac{-x+y}{x+y} times \frac{x+y}{-y+1} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out x+y in both numerator and denominator.

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

Expand

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

Solution Steps

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

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

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

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

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

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

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

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

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

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

Cancel out y in both numerator and denominator.

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

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

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

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

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

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

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

Cancel out x in both numerator and denominator.

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

Multiply \frac{-x+y}{x+y} times \frac{x+y}{-y+1} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out x+y in both numerator and denominator.

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