\[{x^2} + \frac{1}{{{x^2}}} + \frac{1}{2}\left( {x - \frac{1}{x}} \right) = 5\]

\[{\text{Решите уравнение: }}\frac{1}{x} + \frac{1}{{x + 1}} + \frac{1}{{x + 2}} = \frac{2}{3}.\]