[tex] \frac{ \sqrt{(2p+1)^3} + \sqrt{(2p-1)^3} }{ \sqrt{4p+2 \sqrt{4p^2-1} } } =[/tex]
[tex]=\frac{[\sqrt{(2p+1)} +\sqrt{(2p-1)}] [\sqrt{(2p+1)}^2 +\sqrt{(2p-1)}^2-\sqrt{(2p+1)} *\sqrt{(2p-1)}] }{ \sqrt{ (2p+1)+ (2p-1) +2 \sqrt{(2p+1)(2p-1)} } }=[/tex]
[tex]=\frac{[\sqrt{(2p+1)} +\sqrt{(2p-1)}] [4p-\sqrt{(4p^2-1)} ] }{ \sqrt{[ \sqrt{(2p+1)} +\sqrt{(2p-1)} ]^2 } } =[/tex]
[tex]=\frac{[\sqrt{(2p+1)} +\sqrt{(2p-1)}] [4p-\sqrt{(4p^2-1)} ] }{ [\sqrt{(2p+1)} +\sqrt{(2p-1)} ]} = [/tex]
[tex]=4p-\sqrt{(4p^2-1)} [/tex]
