Answer:
[tex]-3+2\sqrt{2}[/tex]
Step-by-step explanation:
[tex]\frac{\sqrt{3} -\sqrt{6}}{\sqrt{3} +\sqrt{6}}[/tex]
[tex]=\frac{(\sqrt{3} -\sqrt{6})(\sqrt{3} -\sqrt{6})}{(\sqrt{3} +\sqrt{6})(\sqrt{3} -\sqrt{6})}[/tex]
[tex]=\frac{9-6\sqrt{2} }{-3}[/tex]
[tex]=\frac{3(3-2\sqrt{2} )}{-3}[/tex]
[tex]=-(3-2\sqrt{2})[/tex]
[tex]=-3+2\sqrt{2}[/tex]
