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

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

Evaluate

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

Short Solution Steps

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

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

Since \frac{x-1}{x+1} and \frac{x+1}{x+1} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in x-1-\left(x+1\right).

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

Combine like terms in x-1-x-1.

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

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

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

Since \frac{x-1}{x+1} and \frac{x+1}{x+1} have the same denominator, add them by adding their numerators.

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

Combine like terms in x-1+x+1.

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

Divide \frac{-2}{x+1} by \frac{2x}{x+1} by multiplying \frac{-2}{x+1} by the reciprocal of \frac{2x}{x+1}.

$$\frac{-2\left(x+1\right)}{\left(x+1\right)\times 2x}$$

Cancel out 2\left(x+1\right) in both numerator and denominator.

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

Expand

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

Short Solution Steps

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

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

Since \frac{x-1}{x+1} and \frac{x+1}{x+1} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in x-1-\left(x+1\right).

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

Combine like terms in x-1-x-1.

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

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

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

Since \frac{x-1}{x+1} and \frac{x+1}{x+1} have the same denominator, add them by adding their numerators.

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

Combine like terms in x-1+x+1.

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

Divide \frac{-2}{x+1} by \frac{2x}{x+1} by multiplying \frac{-2}{x+1} by the reciprocal of \frac{2x}{x+1}.

$$\frac{-2\left(x+1\right)}{\left(x+1\right)\times 2x}$$

Cancel out 2\left(x+1\right) in both numerator and denominator.

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