$3 \cdot 3$ Simplify the fraction $\frac{x^{8}+x^{6}+x^{4}+x^{2}+1}{x^{4}+x^{3}+x^{2}+x+1}$, and calculate the value of the fraction when $x=-0.02$.
[Solution]
$$
\begin{aligned}
\text { Original expression } & =\frac{x^{10}-1}{x^{2}-1} \div \frac{x^{5}-1}{x-1} \\
& =\frac{x^{5}+1}{x+1} \\
& =x^{4}-x^{3}+x^{2}-x+1 .
\end{aligned}
$$

When $x=-0.02$,
$$
\text { Original expression }=\frac{312499999}{306250000} \text {. }
$$