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Simplify and rationalize the denominator:

 

$\cfrac{1}{1+ \cfrac{1}{\sqrt{3}+2}}.$

 Sep 19, 2021
 #1
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\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.

 Sep 20, 2021

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