:[latex]1) \frac{n+2+ \sqrt{n^2-4} }{n+2- \sqrt{n^2-4} } + \frac{n+2- \sqrt{n^2-4} }{n+2+ \sqrt{n^2-4} } [/latex][latex]2) \frac{a}{ \sqrt{1- \frac{b^2}{a^2} } } -b \sqrt{ \frac{a^2}{b^2} } -1+ \frac{b}{ \sqrt{ \frac{a^2}{b^2} ...

Question

:[latex]1) \frac{n+2+ \sqrt{n^2-4} }{n+2- \sqrt{n^2-4} } + \frac{n+2- \sqrt{n^2-4} }{n+2+ \sqrt{n^2-4} } [/latex][latex]2) \frac{a}{ \sqrt{1- \frac{b^2}{a^2} } } -b \sqrt{ \frac{a^2}{b^2} } -1+ \frac{b}{ \sqrt{ \frac{a^2}{b^2} ...

:[latex]1) \frac{n+2+ \sqrt{n^2-4} }{n+2- \sqrt{n^2-4} } + \frac{n+2- \sqrt{n^2-4} }{n+2+ \sqrt{n^2-4} } [/latex][latex]2) \frac{a}{ \sqrt{1- \frac{b^2}{a^2} } } -b \sqrt{ \frac{a^2}{b^2} } -1+ \frac{b}{ \sqrt{ \frac{a^2}{b^2} }-1 } .[/latex]

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Accepted Answer

[latex] \frac{(n+2+\sqrt{n^{2}-4})^{2}+(n+2-\sqrt{n^{2}-4})^{2}}{(n+2)^{2}-(\sqrt{n^{2}-4})^{2}}= \frac{2(n+2)^{2}+2(n^{2}-4)}{n^{2}+4n+4-n^{2}+4}= \frac{2(n^{2}+4n+4+n^{2}-4)}{4(n+4)}= \frac{4n(n+2)}{4(n+4)}= \frac{n(n+2)}{n+4} [/latex]