#Murad
$A=\dfrac{1}{\sqrt{3}+1}+\dfrac{1}{\sqrt{3}-1}$
$=\dfrac{\sqrt{3}-1+\sqrt{3}+1}{(\sqrt{3}+1)(\sqrt{3}-1)}$
$=\dfrac{2\sqrt{3}}{3-1}$
$=\sqrt{3}$
$B=\dfrac{1}{1-\sqrt{2}}+\dfrac{1}{1+\sqrt{2}}$
$=\dfrac{1+\sqrt{2}+1-\sqrt{2}}{(1-\sqrt{2})(1+\sqrt{2})}$
$=\dfrac{2}{1-2}$
$=-2$
$C=\dfrac{5+\sqrt{5}}{5-\sqrt{5}}+\dfrac{5-\sqrt{5}}{5+\sqrt{5}}$
$=\dfrac{(5+\sqrt{5})^2}{(5-\sqrt{5})(5+\sqrt{5})}+\dfrac{(5-\sqrt{5})^2}{(5+\sqrt{5})(5-\sqrt{5})}$
$=\dfrac{25+10\sqrt{5}+5+25-10\sqrt{5}+5}{(5+\sqrt{5})(5-\sqrt{5})}$
$=\dfrac{60}{25-5}$
$=\dfrac{60}{20}$
$=3$
$D=\dfrac{\sqrt{3}}{\sqrt{\sqrt{3}+1}-1}-\dfrac{\sqrt{3}}{\sqrt{\sqrt{3}+1}+1}$
$=\dfrac{\sqrt{3}(\sqrt{\sqrt{3}+1}+1)-\sqrt{3}(\sqrt{\sqrt{3}+1}-1)}{(\sqrt{\sqrt{3}+1}-1)(\sqrt{\sqrt{3}+1}+1)}$
$=\dfrac{\sqrt{3+\sqrt{3}}+\sqrt{3}-\sqrt{3+\sqrt{3}}+\sqrt{3}}{\sqrt{3}+1-1}$
$=\dfrac{2\sqrt{3}}{\sqrt{3}}$
$=2$
