To simplify the expression \(\frac{1}{\sqrt{3}+2}\) in the form \(a+b\sqrt{3}\), we can rationalize the denominator by multiplying both the numerator and denominator by the conjugate of the denominator, which is \(\sqrt{3}-2\). This gives us:

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

So, the simplified form of the expression is \(-\sqrt{3}+2\), which can also be written as \(2-\sqrt{3}\).