[tex] \frac{ \sqrt{x+2}+ \sqrt{x-2} }{ \sqrt{x+2}- \sqrt{x-2} } = \frac{( \sqrt{x+2}+ \sqrt{x-2} )*( \sqrt{x+2}+ \sqrt{x-2} ) }{ (\sqrt{x+2}- \sqrt{x-2})*( \sqrt{x+2}+ \sqrt{x-2} ) } = \frac{ (\sqrt{x+2}+ \sqrt{x-2})^2 }{ (\sqrt{x+2})^2- (\sqrt{x-2})^2 } = \\ \\ = \frac{ x+2+2 \sqrt{(x+2)(x-2)}+x-2 }{ x+2-(x-2) } = \frac{ 2x+2 \sqrt{x^2-4} }{ x+2-x+2 } = \frac{ 2(x+\sqrt{x^2-4}) }{4} = \frac{ x+\sqrt{x^2-4} }{2} [/tex]
