Đáp án: `\frac{3\sqrt{21} +6\sqrt{3} +\sqrt{42} +2\sqrt{6}}{3}`
Giải thích các bước giải:
`\frac{\sqrt{3} + \sqrt{6} +\sqrt{12}}{\sqrt{7} -2}`
`= \frac{\sqrt{3} + \sqrt{6} +2\sqrt{3}}{\sqrt{7} -2}`
`= \frac{3\sqrt{3} +\sqrt{6}}{\sqrt{7}-2}`
`= \frac{(3\sqrt{3} +\sqrt{6})(\sqrt{7}+2)}{(\sqrt{7} -2)(\sqrt{7}+2)}`
`= \frac{3\sqrt{21} +6\sqrt{3} +\sqrt{42} +2\sqrt{6}}{(\sqrt{7})^2 -2²}`
`=\frac{3\sqrt{21} +6\sqrt{3} +\sqrt{42} +2\sqrt{6}}{3}`