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Simplify and rationalize the denominator: 1/(1 + 1/(sqrt(3) + 2)).

 Jul 17, 2021
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\(\begin{align*} \frac{1}{1+\frac{1}{\sqrt{3}+2}} &= \frac{1}{\frac{3+\sqrt{3}}{\sqrt{3}+2}} \\ &= \frac{\sqrt{3}+2}{3+\sqrt{3}} \\ &= \boxed{\frac{3+\sqrt{3}}{6}} \end{align*}\)

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 Jul 17, 2021

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