Solve x^2+1/x^2-3

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

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x^{2}-3 times \frac{x^{2}}{x^{2}}.

$$\frac{\left(x^{2}-3\right)x^{2}}{x^{2}}+\frac{1}{x^{2}}$$

Since \frac{\left(x^{2}-3\right)x^{2}}{x^{2}} and \frac{1}{x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\left(x^{2}-3\right)x^{2}+1}{x^{2}}$$

Do the multiplications in \left(x^{2}-3\right)x^{2}+1.

$$\frac{x^{4}-3x^{2}+1}{x^{2}}$$

Factor

$$\frac{\left(x^{2}-\frac{3-\sqrt{5}}{2}\right)\left(x^{2}-\frac{\sqrt{5}+3}{2}\right)}{x^{2}}$$