Solve p-2+1/p^2

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

Evaluate

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

Short Solution Steps

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

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

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

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

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

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

Factor

$$\frac{\left(p-1\right)\left(p-\frac{1-\sqrt{5}}{2}\right)\left(p-\frac{\sqrt{5}+1}{2}\right)}{p^{2}}$$