Simplify \(\frac{1}{\sqrt{3}+2}\) in the form \(a+b\sqrt{3}\)

Explanation

\(\frac{1}{\sqrt{3}+2}=\frac{1}{\sqrt{3}+2}\times \frac{\sqrt{3}-2}{\sqrt{3}-2}\\=\frac{\sqrt{3}-2}{(\sqrt{3})^{2} -2^{2}}\\=\frac{\sqrt{3}-2}{3-4}=\frac{\sqrt{3}-2}{1}\\=-\sqrt{3}+2\\=2-\sqrt{3}\)