Example 1 Given $a b c \neq 0$, and $a+b+c=0$. Then the value of the algebraic expression $\frac{a^{2}}{b c}+\frac{b^{2}}{a c}+\frac{c^{2}}{a b}$ is ( ).
(A) 3
(B) 2
(C) 1
(D) 0
Solution 1 Original expression
$$
\begin{array}{l}
=\frac{-(b+c) a}{b c}+\frac{-(a+c) b}{a c}+\frac{-(a+b) c}{a b} \\
=-\left(\frac{a}{b}+\frac{a}{c}\right)-\left(\frac{b}{a}+\frac{b}{c}\right)-\left(\frac{c}{a}+\frac{c}{b}\right) \\
=3 .
\end{array}
$$

Solution 2 Given $a+b+c=0$, we can take
$$
a=b=1, c=-2 \text {. }
$$

Substituting directly, we get
$$
\text { Original expression }=-\frac{1}{2}-\frac{1}{2}+4=3 \text {. }
$$

Therefore, the answer is A.