Solve (x+y/x-y-1)/(1-frac{x+y{x-y})}=

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

Evaluate

$$-1$$

Short Solution Steps

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

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

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

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

Do the multiplications in x+y-\left(x-y\right).

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

Combine like terms in x+y-x+y.

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

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

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

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

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

Do the multiplications in x-y-\left(x+y\right).

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

Combine like terms in x-y-x-y.

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

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

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

Cancel out 2y\left(x-y\right) in both numerator and denominator.

$$\frac{1}{-1}$$

Divide 1 by -1 to get -1.

$$-1$$

Factor

$$-1$$