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

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

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{x}{x}.

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

Since \frac{2x}{x} and \frac{1+x^{2}}{x} have the same denominator, add them by adding their numerators.

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

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

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

Factor the expressions that are not already factored.

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

Cancel out x+1 in both numerator and denominator.

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

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{x}{x}.

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

Since \frac{2x}{x} and \frac{1+x^{2}}{x} have the same denominator, add them by adding their numerators.

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

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

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

Factor the expressions that are not already factored.

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

Cancel out x+1 in both numerator and denominator.

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