[tex]\displaystyle\bf\\7) \ \ \frac{\sqrt{3} +\sqrt{2} }{\sqrt{3}-\sqrt{2} }=\frac{(\sqrt{3} +\sqrt{2})\cdot(\sqrt{3} +\sqrt{2}) }{(\sqrt{3}-\sqrt{2} )\cdot(\sqrt{3} +\sqrt{2} ) } =\frac{3+2\sqrt{6} +2}{(\sqrt{3} )^{2} -(\sqrt{2} )^{2} } =\\\\\\=\frac{5+2\sqrt{6} }{3-2} =5+2\sqrt{6} \\\\\\5) \ \ \frac{2}{\sqrt{3} -1} =\frac{2\cdot(\sqrt{3} +1)}{(\sqrt{3} -1)\cdot(\sqrt{3} +1)} =\frac{2\cdot(\sqrt{3} +1)}{(\sqrt{3})^{2} -1^{2} } =[/tex]
[tex]\displaystyle\bf\\=\frac{2\cdot(\sqrt{3} +1)}{3-1} =\frac{2\cdot(\sqrt{3} +1)}{2} =\sqrt{3} +1[/tex]
