\[ \cfrac{1}{2 + \sqrt{3}} \] \[ = \cfrac{(2 - \sqrt{3})}{(2 + \sqrt{3})(2 - \sqrt{3})} \] \[ = \cfrac{2 - \sqrt{3}}{4 - 3} \] \[ = \cfrac{2 - \sqrt{3}}{1} \] \[ = 2 - \sqrt{3} \]
\[ \cfrac{1}{2 + \sqrt{3}} \] \[ = \cfrac{(2 - \sqrt{3})}{(2 + \sqrt{3})(2 - \sqrt{3})} \] \[ = \cfrac{2 - \sqrt{3}}{4 - 3} \] \[ = \cfrac{2 - \sqrt{3}}{1} \] \[ = 2 - \sqrt{3} \]