Solve x/1+x^2+1/x=

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

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 1+x^{2} and x is x\left(x^{2}+1\right). Multiply \frac{x}{1+x^{2}} times \frac{x}{x}. Multiply \frac{1}{x} times \frac{x^{2}+1}{x^{2}+1}.

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

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

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

Do the multiplications in xx+x^{2}+1.

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

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

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

Expand x\left(x^{2}+1\right).

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

Factor

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