1 - 76 Rationalize the numerator of $\frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}}$, then the simplest form of its denominator is
(A) $\sqrt{3}(\sqrt{3}+\sqrt{2})$.
(B) $\sqrt{3}(\sqrt{3}-\sqrt{2})$.
(C) $3-\sqrt{3} \sqrt{2}$.
(D) $3+\sqrt{6}$.
(E) None of the above answers is correct.
(1st American High School Mathematics Examination, 1950)
$$
\text { [Solution] } \begin{aligned}
\text { Original expression } & =\frac{(\sqrt{3}-\sqrt{2})(\sqrt{3}+\sqrt{2})}{\sqrt{3}(\sqrt{3}+\sqrt{2})}=\frac{3-2}{\sqrt{3}(\sqrt{3}+\sqrt{2})} \\
& =\frac{1}{3+\sqrt{6} .}
\end{aligned}
$$

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