Answer:
[tex]6-2\sqrt{6}[/tex]
Step-by-step explanation:
[tex]x=\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}[/tex]
[tex]x= \frac{\left(\sqrt{3}+\sqrt{2}\right)\left(\sqrt{3}+\sqrt{2}\right)}{\left(\sqrt{3}-\sqrt{2}\right)\left(\sqrt{3}+\sqrt{2}\right)}[/tex]
[tex]x=\frac{5+2\sqrt{6}}{1}[/tex]
[tex]x=5+2\sqrt{6}[/tex]
Substitute [tex]5+2\sqrt{6}[/tex] for [tex]x[/tex].
[tex]\frac{x+1}{x}[/tex]
[tex]\frac{5+2\sqrt{6}+1}{5+2\sqrt{6}}[/tex]
[tex]\frac{6+2\sqrt{6}}{5+2\sqrt{6}}[/tex]
[tex]\frac{\left(6+2\sqrt{6}\right)\left(5-2\sqrt{6}\right)}{\left(5+2\sqrt{6}\right)\left(5-2\sqrt{6}\right)}[/tex]
[tex]\frac{6-2\sqrt{6}}{1}[/tex]
[tex]6-2\sqrt{6}[/tex]
