Question

rút gọn :\(12\sqrt{\frac{4}{3}}-\frac{8+2\sqrt{2}}{3-\sqrt{2}}-\frac{4-6\sqrt{2}}{\sqrt{2}}+\frac{\sqrt{3}}{\sqrt{3}-2}\)

Answer 1

\(12\sqrt{\frac{4}{3}}-\frac{8+2\sqrt{2}}{3-\sqrt{2}}-\frac{4-6\sqrt{2}}{\sqrt{2}}+\frac{\sqrt{3}}{\sqrt{3}-2}\)

\(=12.\frac{2}{\sqrt{3}}-\frac{\left(3+\sqrt{2}\right)\left(8-2\sqrt{2}\right)}{9-2}-\frac{\sqrt{2}\left(4-6\sqrt{2}\right)}{2}+\frac{\sqrt{3}\left(\sqrt{3}-2\right)}{3-4}\)

\(=8\sqrt{3}-\left(4+2\sqrt{2}\right)-\left(2\sqrt{2}-6\right)+\left(-3-2\sqrt{3}\right)\)

\(=8\sqrt{3}-4-2\sqrt{2}-2\sqrt{2}+6-3-2\sqrt{3}\)

\(=6\sqrt{3}-4\sqrt{2}-1\)