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

 Oct 11, 2022
 #1
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\(1\over1+{1\over\sqrt{3}}+2\)

Multiply top and bottom by root3 and combine 1 + 2.

\(\sqrt{3}\over3\sqrt{3}+1\)

Multiply top and bottom by \(3\sqrt{3}-1\)

\(\sqrt{3}(3\sqrt{3}-1)\over(3\sqrt{3}+1)(3\sqrt{3}-1)\)

\(9 - \sqrt{3}\over26\)

 Oct 11, 2022
 #2
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That answer is wrong.

Guest Oct 12, 2022

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