Solve y^2-1/y^2+2

$$y ^ { 2 } - \frac { 1 } { y ^ { 2 } } + 2$$

Evaluate

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

Short Solution Steps

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

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

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

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

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

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

Factor

$$\frac{\left(y^{2}-\left(-\sqrt{2}-1\right)\right)\left(y^{2}-\left(\sqrt{2}-1\right)\right)}{y^{2}}$$