Question 131
Suppose $x$ is a fifth root of unity. Find, in radical form, all possible values of
$$
2x + \frac{1}{1+x} + \frac{x}{1+x^{2}} + \frac{x^{2}}{1+x^{3}} + \frac{x^{3}}{1+x^{4}}.
$$
$$
2x + \frac{1}{1+x} + \frac{x}{1+x^{2}} + \frac{x^{2}}{1+x^{3}} + \frac{x^{3}}{1+x^{4}}.
$$