[tex]\displaystyle\\
\Big(3\sqrt{2} - 2\sqrt{3}\Big) : \Big(2\sqrt{3} - 3\sqrt{2}\Big) = ?\\\\
\text{comparam numerele }~3\sqrt{2}~\text{ si }~2\sqrt{3}\\\\
\Big(3\sqrt{2}\Big)^2 = 9 \times 2 = 18\\
\Big(2\sqrt{3}\Big)^2 = 4 \times 3 = 12\\
\Longrightarrow~~3\sqrt{2} \ \textgreater \ 2\sqrt{3}\\\\
\Big(3\sqrt{2} - 2\sqrt{3}\Big) \ \textgreater \ 0~\text{ iar }~ \Big(2\sqrt{3} - 3\sqrt{2}\Big)\ \textless \ 0 \\\\
\Longrightarrow~~\Big(2\sqrt{3} - 3\sqrt{2}\Big)= -\Big(3\sqrt{2} - 2\sqrt{3}\Big) \\\\
[/tex]
[tex]\displaystyle\\
\Longrightarrow~\Big(3\sqrt{2} - 2\sqrt{3}\Big) : \Big(2\sqrt{3} - 3\sqrt{2}\Big) =\\\\
= \frac{3\sqrt{2} - 2\sqrt{3}}{2\sqrt{3} - 3\sqrt{2}}= \frac{3\sqrt{2} - 2\sqrt{3}}{-\Big(3\sqrt{2} - 2\sqrt{3}\Big)}=-\frac{3\sqrt{2} - 2\sqrt{3}}{3\sqrt{2} - 2\sqrt{3}}= \boxed{\bf -1}[/tex]
