3. As shown in Figure 1, in

Rt $\triangle A B C$, it is
known that $\angle C=90^{\circ}, C D$
is the altitude. Let $B C=a$,
$$
\begin{array}{l}
C A=b(a \neq b), \\
C D=h, A D=m, \\
D B=n . \text { Let }
\end{array}
$$
$$
f=a m n+b m n, g=a h m+b h n .
$$

Then the relationship between $f$ and $g$ is ( ).
(A) $f>g$
(B) $f<g$
(C) $f=g$
(D) $f \neq g$
3. C.

From the knowledge of similar triangles, we easily get
$$
\begin{array}{l}
\frac{a}{h}=\frac{b}{m}, \frac{b}{h}=\frac{a}{n} \\
\Rightarrow \frac{a+b}{h}=\frac{a}{n}+\frac{b}{m}=\frac{a m+b n}{m n} \\
\Rightarrow a m n+b m n=a h m+b h n .
\end{array}
$$