Example 2 If $a=\frac{19951995}{19961996}, b=\frac{19961996}{19971997}$, $c=\frac{19971997}{19981998}$, then ().
(A) $a<b<c$
(B) $b<c<a$
(C) $c<b<a$
(D) $a<c<b$
Solve: Subtract 1 from each fraction to get
$$
\begin{array}{l}
a-1=-\frac{10001}{19961996}, \\
b-1=-\frac{10001}{19971997}, \\
c-1=-\frac{10001}{19981998} . \\
\text { Since } a-1<b-1<c-1 \\
\Rightarrow a<b<c .
\end{array}
$$

Therefore, the answer is (A).