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

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

Evaluate

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

Short Solution Steps

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

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

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

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

Combine like terms in 1+x-1.

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

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

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

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

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

Combine like terms in 1+x+1.

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

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

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

Cancel out x+1 in both numerator and denominator.

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

Expand

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

Short Solution Steps

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

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

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

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

Combine like terms in 1+x-1.

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

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

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

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

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

Combine like terms in 1+x+1.

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

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

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

Cancel out x+1 in both numerator and denominator.

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