2. Let $x_{1}=1, x_{n}=\frac{x_{n-1}-1}{2 x_{n-1}+4}(n \geqslant 2)$. The general term formula of the sequence $\left\{x_{n}\right\}$ is $x_{n}=$ $\qquad$
$\begin{array}{l}\text { 2. } \frac{2^{n-2}-3^{n-2}}{2 \times 3^{n-2}-2^{n-2}} \text {. } \\ \text { Given } x_{n}+1=3 \frac{x_{n-1}+1}{2 x_{n-1}+4}, 2 x_{n}+1=2 \frac{2 x_{n-1}+1}{2 x_{n-1}+4} \\ \Rightarrow \frac{x_{n}+1}{2 x_{n}+1}=\frac{3}{2} \times \frac{x_{n-1}+1}{2 x_{n-1}+1}=\left(\frac{3}{2}\right)^{n-2} \\ \Rightarrow x_{n}=\frac{2^{n-2}-3^{n-2}}{2 \times 3^{n-2}-2^{n-2}} \text {. }\end{array}$