Solve x^2+1/x^2+6

$${ x }^{ 2 } + \frac{ 1 }{ { x }^{ 2 } } +6$$

Evaluate

$$x^{2}+6+\frac{1}{x^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x^{2}+6 times \frac{x^{2}}{x^{2}}.

$$\frac{\left(x^{2}+6\right)x^{2}}{x^{2}}+\frac{1}{x^{2}}$$

Since \frac{\left(x^{2}+6\right)x^{2}}{x^{2}} and \frac{1}{x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\left(x^{2}+6\right)x^{2}+1}{x^{2}}$$

Do the multiplications in \left(x^{2}+6\right)x^{2}+1.

$$\frac{x^{4}+6x^{2}+1}{x^{2}}$$

Factor

$$\frac{\left(x^{2}-\left(-2\sqrt{2}-3\right)\right)\left(x^{2}-\left(2\sqrt{2}-3\right)\right)}{x^{2}}$$