Question

Rút gọn giúp mình với  

\(\dfrac{24-9\sqrt{3}}{3-\sqrt{3}}\)

Answer 1

\(\dfrac{24-9\sqrt{3}}{3-\sqrt{3}}\)

\(=\dfrac{\sqrt{3}\cdot\left(8\sqrt{3}-9\right)}{\sqrt{3}\cdot\left(\sqrt{3}-1\right)}\)

\(=\dfrac{8\sqrt{3}-9}{\sqrt{3}-1}\)

\(=\dfrac{\left(8\sqrt{3}-9\right)\left(\sqrt{3}+1\right)}{\left(\sqrt{3}-1\right)\left(\sqrt{3}+1\right)}\)

\(=\dfrac{8\cdot3+8\sqrt{3}-9\sqrt{3}-9}{2}\)

\(=\dfrac{15-\sqrt{3}}{2}\)

Answer 2

Tham khảo:

\(\dfrac{15-\sqrt{3}}{2}\)