Question

:$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} }$$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 } .$

Answer 1

$frac{(n+2+sqrt{n^{2}-4})^{2}+(n+2-sqrt{n^{2}-4})^{2}}{(n+2)^{2}-(sqrt{n^{2}-4})^{2}}= frac{2(n+2)^{2}+2(n^{2}-4)}{n^{2}+4n+4-n^{2}+4}= frac{2(n^{2}+4n+4+n^{2}-4)}{4(n+4)}= frac{4n(n+2)}{4(n+4)}= frac{n(n+2)}{n+4}$