Solve omega^17+1/omega^17-1

$$\omega ^ { 17 } + \frac { 1 } { \omega ^ { 17 } } - 1$$

Evaluate

$$\omega ^{17}-1+\frac{1}{\omega ^{17}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply \omega ^{17}-1 times \frac{\omega ^{17}}{\omega ^{17}}.

$$\frac{\left(\omega ^{17}-1\right)\omega ^{17}}{\omega ^{17}}+\frac{1}{\omega ^{17}}$$

Since \frac{\left(\omega ^{17}-1\right)\omega ^{17}}{\omega ^{17}} and \frac{1}{\omega ^{17}} have the same denominator, add them by adding their numerators.

$$\frac{\left(\omega ^{17}-1\right)\omega ^{17}+1}{\omega ^{17}}$$

Do the multiplications in \left(\omega ^{17}-1\right)\omega ^{17}+1.

$$\frac{\omega ^{34}-\omega ^{17}+1}{\omega ^{17}}$$

Factor

$$\frac{\left(\omega ^{2}-\omega +1\right)\left(\omega ^{32}+\omega ^{31}-\omega ^{29}-\omega ^{28}+\omega ^{26}+\omega ^{25}-\omega ^{23}-\omega ^{22}+\omega ^{20}+\omega ^{19}-\omega ^{17}-\omega ^{16}-\omega ^{15}+\omega ^{13}+\omega ^{12}-\omega ^{10}-\omega ^{9}+\omega ^{7}+\omega ^{6}-\omega ^{4}-\omega ^{3}+\omega +1\right)}{\omega ^{17}}$$