[tex]=\frac{\sqrt{5}-\sqrt{3}}{(\sqrt{5}+\sqrt{3})(\sqrt{5}-\sqrt{3})}+\frac{\sqrt{7}-\sqrt{5}}{(\sqrt{7}-\sqrt{5})(\sqrt{7}+\sqrt{5})}+...+\frac{\sqrt{99}-\sqrt{97}}{(\sqrt{99}-\sqrt{97})(\sqrt{99}+\sqrt{97})} =\frac{\sqrt{5}-\sqrt{3}+\sqrt{7}-\sqrt{5}+..+\sqrt{99}-\sqrt{97}}{2} =-\sqrt{3}+\sqrt{99}[/tex]