Question

Answer 1

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

Answer 2

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

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

=1+1+1

=3