Question

A = (sqrt(4 + 2sqrt(3)) - 1)/(sqrt(4 + 2sqrt(3)) +2)

Answer 1

\(A=\dfrac{\sqrt{4-2\sqrt{3}}-1}{\sqrt{4+2\sqrt{3}}+2}\)

\(A=\dfrac{\sqrt{\left(\sqrt{3}\right)^2+2\cdot\sqrt{3}\cdot1+1^2}-1}{\sqrt{\left(\sqrt{3}\right)^2+2\cdot\sqrt{3}\cdot1+1^2}+2}\)

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

\(A=\dfrac{\left|\sqrt{3}+1\right|+1}{\left|\sqrt{3}+1\right|-2}\)

\(A=\dfrac{\sqrt{3}+1+1}{\sqrt{3}+1-2}\)  

\(A=\dfrac{\sqrt{3}+2}{\sqrt{3}-1}\)

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

\(A=\dfrac{3+\sqrt{3}+2\sqrt{3}+2}{3-1}\)

\(A=\dfrac{5+3\sqrt{3}}{2}\)

Answer 2

A = \(\dfrac{5+3\sqrt{3}}{2}\)