Question

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

Answer 1

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

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

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

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

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

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

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

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