Question

Thực hiện phép tínhc/ 2/(sqrt(3) - 1) - (3 + sqrt(3))/(sqrt(3) + 1)

Answer 1

\(\dfrac{2}{\sqrt{3}-1}-\dfrac{3\sqrt{3}}{\sqrt{3}+1}\\ =\dfrac{2\left(\sqrt{3}+1\right)}{\left(\sqrt{3}-1\right)\left(\sqrt{3}+1\right)}-\dfrac{3\sqrt{3}\left(\sqrt{3}-1\right)}{\left(\sqrt{3}+1\right)\left(\sqrt{3}-1\right)}\\ =\dfrac{2\left(\sqrt{3}+1\right)-3\sqrt{3}\left(\sqrt{3}-1\right)}{\left(\sqrt{3}-1\right)\left(\sqrt{3}+1\right)}\\ =\dfrac{2\sqrt{3}+2-9+3\sqrt{3}}{2}\\ =\dfrac{5\sqrt{3}-7}{2}\)