Example 1. If $x=2-\sqrt{3}$, find the value of $\frac{x^{4}-4 x^{3}-x^{2}+9 x-4}{x^{2}-4 x+5}$.
(1989, Shanghai Junior High School Mathematics Competition)
Solve $x=2-\sqrt{3}, x-2=-\sqrt{3}$, square both sides, we get
$$
\begin{aligned}
& x^{2}-4 x+1=0 . \\
\text { Then } & \frac{x^{4}-4 x^{3}-x^{2}+9 x-4}{x^{2}-4 x+5} \\
= & \frac{x^{2}\left(x^{2}-4 x+1\right)-2\left(x^{2}-4 x+1\right)+x-2}{\left(x^{2}-4 x+1\right)+4} \\
= & \frac{x^{2} \cdot 0-2 \cdot 0+x-2}{0+4} \\
= & \frac{x-2}{4}=-\frac{\sqrt{3}}{4} .
\end{aligned}
$$

Note: This problem constructs an expression $x^{2}-4 x+1$ that equals 0, and transforms the required expression to include $x^{2}-4 x+1$, then uses 0 substitution to solve.