Solve (a^2+1/a^2)-4

$$( a ^ { 2 } + \frac { 1 } { a ^ { 2 } } ) - 4$$

Evaluate

$$a^{2}-4+\frac{1}{a^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply a^{2}-4 times \frac{a^{2}}{a^{2}}.

$$\frac{\left(a^{2}-4\right)a^{2}}{a^{2}}+\frac{1}{a^{2}}$$

Since \frac{\left(a^{2}-4\right)a^{2}}{a^{2}} and \frac{1}{a^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\left(a^{2}-4\right)a^{2}+1}{a^{2}}$$

Do the multiplications in \left(a^{2}-4\right)a^{2}+1.

$$\frac{a^{4}-4a^{2}+1}{a^{2}}$$

Factor

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