8.12 Let $75^{x}=0.75^{y}=10^{-2}$, then $\frac{1}{x}-\frac{1}{y}$ equals
(A) $\frac{1}{4}$.
(B) $-\frac{1}{4}$.
(C) 1 .
(D) -1 .
(China Partial Provinces and Cities Junior High School Mathematics Correspondence Competition, 1987)
[Solution] From the given, we have $75^{x y}=10^{-2 y}$,
and
$$
(0.75)^{x y}=\left(\frac{75}{100}\right)^{x y}=10^{-2 x},
$$

which means
$$
75^{x y}=100^{x y} \cdot 10^{-2 x} .
$$

From (1) and (2), we get
$$
100^{x y} \cdot 10^{-2 x}=10^{-2 y} \text {, }
$$

which means
then
which means
thus
$$
\begin{array}{c}
10^{2 x y-2 x}=10^{-2 y}, \\
x y=x-y, \\
1=\frac{1}{y}-\frac{1}{x} .
\end{array}
$$

Therefore, the answer is $(D)$.