Solve (1+1/x)*x/x^2+2x+1

$$( 1 + \frac { 1 } { x } ) \cdot \frac { x } { x ^ { 2 } + 2 x + 1 }$$

Evaluate

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

Short Solution Steps

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

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

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

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

Multiply \frac{x+1}{x} times \frac{x}{x^{2}+2x+1} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out x in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out x+1 in both numerator and denominator.

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

Expand

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

Short Solution Steps

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

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

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

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

Multiply \frac{x+1}{x} times \frac{x}{x^{2}+2x+1} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out x in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out x+1 in both numerator and denominator.

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