Solve x^2+frac{1}x^2+2

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

Evaluate

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

Short Solution Steps

To raise \frac{1}{x} to a power, raise both numerator and denominator to the power and then divide.

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

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

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

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

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

Do the multiplications in \left(x^{2}+2\right)x^{2}+1^{2}.

$$\frac{x^{4}+2x^{2}+1^{2}}{x^{2}}$$

Combine like terms in x^{4}+2x^{2}+1^{2}.

$$\frac{x^{4}+2x^{2}+1}{x^{2}}$$

Factor

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