2.6. The rational function $R(x)=\frac{\left(x^{2}-x+1\right)^{3}}{x^{2}(x-1)^{2}}$ transforms into itself when $x$ is replaced by $1 / x$ or $1-x$. Therefore, the equation under consideration has roots $a, 1 / a, 1-a, 1 /(1-a), 1-1 / a$ and $a /(1-a)$.

For $a>1$, all these six numbers are distinct. The equation under consideration has degree 6, so it cannot have more than six roots.
2.6. Solve the equation $\frac{\left(x^{2}-x+1\right)^{3}}{x^{2}(x-1)^{2}}=\frac{\left(a^{2}-a+1\right)^{3}}{a^{2}(a-1)^{2}}$, where $a>1$.