Correct option is (C) 2√3
\(\because\) \(x=2+\sqrt{3}\)
\(\therefore\) \(\frac1x=\frac1{2+\sqrt{3}}\) \(=\frac1{2+\sqrt{3}}\times\frac{2-\sqrt{3}}{2-\sqrt{3}}\)
\(=\frac{2-\sqrt{3}}{4-3}\) \(=2-\sqrt{3}\)
\(\therefore\) \(x-\frac1x=2+\sqrt{3}-(2-\sqrt{3})=2\sqrt{3}\)