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# help math

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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