$2.2 \frac{x+2}{x+1}+\frac{x+6}{x+3}+\frac{x+10}{x+5}=6$.
2.2 Rewriting the equation as

$$
1+\frac{1}{x+1}+1+\frac{3}{x+3}+1+\frac{5}{x+5}=6
$$

we get

$$
\frac{1}{x+1}+\frac{3}{x+3}+\frac{5}{x+5}=3
$$

From here, bringing to a common denominator, we have

$$
\begin{aligned}
& 9 x^{2}+46 x+45=3 x^{3}+27 x^{2}+69 x+45 \\
& 3 x^{3}+18 x^{2}+23 x=0 ; x\left(3 x^{2}+18 x+23\right)=0 \\
& x_{1}=0 ; x_{2,3}=-3 \pm \frac{2}{3} \sqrt{3}
\end{aligned}
$$

Answer: $\quad x_{1}=0 ; x_{2,3}=-3 \pm \frac{2}{3} \sqrt{3}$.