Question

\(\dfrac{\text{1}}{2+\sqrt{3}}+\sqrt{3}\)

 

Answer 1

\(\dfrac{1}{2+\sqrt{3}}+\sqrt{3}=\dfrac{1+\sqrt{3}\left(2+\sqrt{3}\right)}{2+\sqrt{3}}=\dfrac{1+2\sqrt{3}+3}{2+\sqrt{3}}=\dfrac{\left(1+\sqrt{3}\right)^2}{2+\sqrt{3}}\)

Answer 2

1/(2 + √3) + √3

= (2 - √3)/[(2 + √3)(2 - √3)] + √3

= 2 - √3 + √3

= 2