Example 2. Add a figure, in $\triangle A B C$, $D, E$ are the trisection points on $B C$, point $M$ is the midpoint of $A C$, $B M$ intersects $A D$ at $G$,
intersects $A E$ at $H$. Then
$$
\begin{array}{l}
B G: G H: H M \\
=(\quad) .
\end{array}
$$
(A) $3: 2: 1$
(B) $4: 2: 1$
(C) $5:$
(D) $5: 3: 2$
Analysis: Consider $\triangle A B C$ as the basic triangle. Given that $M$ and $D$ are section points, from (*) we can get
$$
\frac{B G}{G M}=(1+1) \cdot \frac{1}{2}=1,
$$

thus $B G=G M$.
Similarly, in $\triangle A B C$, $\frac{B H}{H M}=(1+1) \cdot 2$ $=4$. Therefore,
$$
\begin{array}{l}
B G+G H=B G+(B G-H M) \\
=2 B G-H M=4 H M .
\end{array}
$$

Thus, $\frac{B M}{H M}=\frac{5}{2}, \frac{B M}{G H}=\frac{5}{3}$. Hence, the answer should be (D).