Solve (x+1)/1-frac{1{x^2+1}}

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

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x^{2}+1}{x^{2}+1}.

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

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

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

Combine like terms in x^{2}+1-1.

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

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

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

Use the distributive property to multiply x+1 by x^{2}+1.

$$\frac{x^{3}+x+x^{2}+1}{x^{2}}$$

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x^{2}+1}{x^{2}+1}.

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

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

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

Combine like terms in x^{2}+1-1.

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

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

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

Use the distributive property to multiply x+1 by x^{2}+1.

$$\frac{x^{3}+x+x^{2}+1}{x^{2}}$$