Question

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

Answer 1

`A=(1/(2-sqrt3)-1/(2+sqrt3)).(sqrt3-1)/(3-sqrt3)`

`=((2+sqrt3)/(4-3)-(2-sqrt3)/(4-3)).((sqrt3-1)/(sqrt3(sqrt3-1)))`

`=(2+sqrt3-2+sqrt3).1/(sqrt3)`

`=2sqrt3. 1/sqrt3`

`=2`

Answer 2

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

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

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