Ta có:
\(\dfrac{1}{2+\sqrt{3}}+\dfrac{1}{2-\sqrt{3}}\)
\(=\dfrac{2-\sqrt{3}}{(2+\sqrt{3})(2-\sqrt{3})}+\dfrac{2+\sqrt{3}}{(2-\sqrt{3})(2+\sqrt{3})}\)
\(=\dfrac{2-\sqrt{3}}{2^2-(\sqrt 3)^2}+\dfrac{2+\sqrt{3}}{2^2-(\sqrt 3)^2}\)
\(=\dfrac{2-\sqrt{3}}{4-3}+\dfrac{2+\sqrt{3}}{4-3}\)
\(=\dfrac{2-\sqrt{3}}{1}+\dfrac{2+\sqrt{3}}{1}\)
\(=2-\sqrt{3}+2+\sqrt{3}=4\).
Chọn đáp án (D). \(4\)
