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

 Oct 12, 2022
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\(1/(1 + 1/(sqrt(3) + 2))\\ =\frac{1}{1 + \frac{1}{(\sqrt3 + 2)}}\\ =1\div( 1 + \frac{1}{(\sqrt3 + 2)})\\ =1\div( \frac{\sqrt3+2+1}{(\sqrt3 + 2)})\\ =1\div \frac{3+\sqrt3}{2+\sqrt3 }\\\)

 

Invert and multiply

then

multiply top and bottom by the conjugate of the bottom.

 

Can you take it from there?

 Oct 12, 2022

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