$1 \cdot 3$ Simplify $\frac{a^{2}-b^{2}}{a b}-\frac{a b-b^{2}}{a b-a^{2}}$ to the simplest term is
(A) $\frac{a}{b}$.
(B) $\frac{a^{2}-2 b^{2}}{a b}$.
(C) $a^{2}$.
(D) $a-2 b$.
(E) None of the above answers is correct.
(1st American High School Mathematics Examination, 1950)
$$
\begin{array}{l}
\text { [Solution] Original expression }=\frac{a^{2}-b^{2}}{a b}-\frac{b(a-b)}{a(b-a)}=\frac{a^{2}-b^{2}}{a b}+\frac{b}{a} \\
=\frac{a^{2}-b^{2}+b^{2}}{a b}=\frac{a^{2}}{a b}=\frac{a}{b}, \\
\end{array}
$$

Therefore, the correct choice is $(A)$.