[tex]\displaystyle \\
m= \Big(\frac{2}{\sqrt{2} }-\frac{3}{\sqrt{3}}\Big)\Big(\sqrt{2}+\sqrt{3}\Big)= \\ \\
=\Big(\frac{2\times \sqrt{2} }{\sqrt{2} \times \sqrt{2}}-\frac{3\times \sqrt{3}}{\sqrt{3}\times \sqrt{3}}\Big)\Big(\sqrt{2}+\sqrt{3}\Big)= \\ \\
=\Big(\frac{2\times \sqrt{2} }{2}-\frac{3\times \sqrt{3}}{3}}\Big)\Big(\sqrt{2}+\sqrt{3}\Big)= \\ \\
=\Big(\sqrt{2} -\sqrt{3}}\Big)\Big(\sqrt{2}+\sqrt{3}\Big)= \\ \\
=(\sqrt{2})^2 - (\sqrt{3})^2 = 2-3 = \boxed{-1 \in Z }
[/tex]
