Simplify and rationalize the denominator: 1/(1 + 1/(sqrt(3) + 2)).
\(\frac{1}{1 + \frac{1}{\sqrt{3} + 2}}\\ =\frac{1}{\frac{\sqrt3+2+1}{\sqrt{3} + 2}}\\ =\frac{1}{\frac{3+\sqrt3}{2+\sqrt{3} }}\\ =\frac{2+\sqrt3}{3+\sqrt3}\\ =\frac{2+\sqrt3}{3+\sqrt3}\times \frac{3-\sqrt3}{3-\sqrt3}\)
etc
