Simplify and rationalize the denominator:
$\cfrac{1}{1+ \cfrac{1}{\sqrt{3}+2}}.$
+118667 \cfrac{1}{1+ \cfrac{1}{\sqrt{3}+2}}.
\(\cfrac{1}{1+ \cfrac{1}{\sqrt{3}+2}}\\ 1\div\left[ 1+\cfrac{1}{\sqrt{3}+2} \right]\\ 1\div\left[ \cfrac{\sqrt3+2+1}{\sqrt{3}+2} \right]\\ 1\div\left[ \cfrac{\sqrt3+3}{\sqrt{3}+2} \right]\\ 1*\left[ \cfrac{\sqrt3+2}{\sqrt{3}+3} \right]\\ \cfrac{\sqrt3+2}{\sqrt{3}+3} * \cfrac{\sqrt3-3}{\sqrt{3}-3} \\ \)
You can check what I have done and take it from there.
