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

 Nov 15, 2021
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\(\frac{1}{1 + \frac{1}{\sqrt{3} + 2}}\\ =\frac{1}{\frac{\sqrt3+2+1}{\sqrt{3} + 2}}\\ =\frac{1}{\frac{3+\sqrt3}{2+\sqrt{3} }}\\ =\frac{2+\sqrt3}{3+\sqrt3}\\ =\frac{2+\sqrt3}{3+\sqrt3}\times \frac{3-\sqrt3}{3-\sqrt3}\)

 

 

etc

 Nov 15, 2021

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