d) D = 5+ căn bậc hai 5/ căn bậc hai 5 + 2 + căn bậc hai 5/ căn bậc hai 5 -1 - 3 căn bậc hai 5/ 3+ căn bậc hai 5

* Hướng dẫn giải

$$\begin{gathered} \mathrm{d}) \mathrm{D}=\frac{5+\sqrt{5}}{\sqrt{5}+2}+\frac{\sqrt{5}}{\sqrt{5}-1}-\frac{3\sqrt{5}}{3+\sqrt{5}}=\frac{\left(5+\sqrt{5}\right)\left(\sqrt{5}-2\right)}{\left(\sqrt{5}+2\right)\left(\sqrt{5}-2\right)}+\frac{\sqrt{5}\left(\sqrt{5}+1\right)}{\left(\sqrt{5}-1\right)\left(\sqrt{5}+1\right)}-\frac{3\sqrt{5}\left(3-\sqrt{5}\right)}{\left(3+\sqrt{5}\right)\left(3-\sqrt{5}\right)} \\ =3\sqrt{5}-5+\frac{{\displaystyle 5+\sqrt{5}}}{{\displaystyle 4}}-\frac{{\displaystyle 9\sqrt{5}-15}}{{\displaystyle 4}}=3\sqrt{5}-5+\frac{{\displaystyle 5+\sqrt{5}-9\sqrt{5}+15}}{{\displaystyle 4}}=3\sqrt{5}-5+5-2\sqrt{5}=\sqrt{5} \\ \mathrm{Vậy} \mathrm{D}=\sqrt{5} \end{gathered}$$