Question

Tính : \(\left(1-\frac{\sqrt{3}-1}{2}\right):\left(\frac{\sqrt{3}-1}{2}+2\right)\)

Answer 1

Đặt  \(\frac{\sqrt{3}-1}{2}=x\). Do đó:  \(\left(1-\frac{\sqrt{3}-1}{2}\right):\left(\frac{\sqrt{3}-1}{2}+2\right)=\frac{1-x}{x+2}=-\frac{x+2-3}{x+2}=-1+\frac{3}{x+2}\)

\(=-1+\frac{3}{\frac{\sqrt{3}-1}{2}+2}=-1+\frac{3}{\frac{\sqrt{3}+3}{2}}=-1+\frac{6}{\sqrt{3}+3}=\frac{-\sqrt{3}+3}{\sqrt{3}+3}=\frac{\sqrt{3}-1}{\sqrt{3}+1}\)  (chia cả tử và mẫu cho  \(\sqrt{3}\)  )

\(=\frac{\left(\sqrt{3}-1\right)^2}{\left(\sqrt{3}+1\right)\left(\sqrt{3}-1\right)}=\frac{4-2\sqrt{3}}{2}=2-\sqrt{3}\)