Giải thích các bước giải:
$C=\dfrac{5+\sqrt{5}}{5-\sqrt{5}}+\dfrac{\sqrt{5}-5}{\sqrt{5}+5}$
$=\dfrac{(5+\sqrt{5})(5+\sqrt{5})}{(5+\sqrt{5})(5-\sqrt{5})}+\dfrac{(\sqrt{5}-5)(\sqrt{5}-5)}{(\sqrt{5}+5)(\sqrt{5}-5)}$
$=\dfrac{30+10\sqrt{5}}{25-5}+\dfrac{30-10\sqrt{5}}{5-25}$
$=\dfrac{15+\sqrt{5}}{2}+\dfrac{\sqrt{5}-15}{2}$
$=\dfrac{15+\sqrt{5}+\sqrt{5}-15}{2}$
$=\dfrac{2\sqrt{5}}{2}$
$=\sqrt{5}$
Vậy $C=\sqrt{5}$
$D=\dfrac{4}{\sqrt{3}+1}+\dfrac{1}{\sqrt{3}-2}+\dfrac{6}{\sqrt{3}-3}$
$=\dfrac{4(\sqrt{3}-1)}{(\sqrt{3}+1)(\sqrt{3}-1)}+\dfrac{\sqrt{3}+2}{(\sqrt{3}+2)(\sqrt{3}-2)}+\dfrac{6(\sqrt{3}+3)}{(\sqrt{3}+3)(\sqrt{3}-3)}$
$=\dfrac{4(\sqrt{3}-1)}{3-1}+\dfrac{\sqrt{3}+2}{3-4}+\dfrac{6(\sqrt{3}+3)}{3-9}$
$=2(\sqrt{3}-1)-\sqrt{3}-2-\sqrt{3}-3$
$=2\sqrt{3}-2-2\sqrt{3}-5$
$=-7$
Vậy $D=-7$
