Rút gọn biểu thức: A=[căn2(3+căn5)]/(2căn2+căn(3+căn5))+[căn2(3−căn5)]/[2căn2−căn(3−căn5

* Hướng dẫn giải

$$\begin{gathered} A=\frac{\sqrt{2}(3+\sqrt{5})}{2\sqrt{2}+\sqrt{3+\sqrt{5}}}+\frac{\sqrt{2}(3-\sqrt{5})}{2\sqrt{2}-\sqrt{3-\sqrt{5}}} \\ 2\left[\frac{3+\sqrt{5}}{4+\sqrt{{(\sqrt{5}+1)}^2}}+\frac{3-\sqrt{5}}{4-\sqrt{{(\sqrt{5}-1)}^2}}\right]=2\left(\frac{3+\sqrt{5}}{5+\sqrt{5}}+\frac{3-\sqrt{5}}{5-\sqrt{5}}\right) \\ 2\left[\frac{(3+\sqrt{5})(5-\sqrt{5})+(3-\sqrt{5})(5+\sqrt{5})}{(5+\sqrt{5})(5-\sqrt{5})}\right]=2\left(\frac{15-3\sqrt{5}+5\sqrt{5}-5+15+3\sqrt{5}-5\sqrt{5}-5}{25-5}\right) \\ =2.\frac{20}{20}=2 \\ Vậy A=2 \end{gathered}$$