Đáp án+Giải thích các bước giải:
`R = (\frac{\sqrt{14} - \sqrt{7}}{\sqrt{2} - 1} + \frac{\sqrt{15} - \sqrt{5}}{\sqrt{3} - 1}) : \frac{1}{\sqrt{7} - \sqrt{5}}`
`= (\frac{\sqrt{7}(\sqrt{2} - 1)}{\sqrt{2} - 1} + \frac{\sqrt{5}(\sqrt{3} - 1)}{\sqrt{3} - 1}) . (\sqrt{7} - \sqrt{5})`
`= (\sqrt{7} + \sqrt{5}) . (\sqrt{7} - \sqrt{5})`
`= 7 - 5 = 2`
`S = (\sqrt{5} + \sqrt{3} - \sqrt{2})(\sqrt{5} + \sqrt{2} - \sqrt{3})`
`= [\sqrt{5} - (\sqrt{2} - \sqrt{3})] . [\sqrt{5} + (\sqrt{2} - \sqrt{3})]`
`= 5 - (2 - 2\sqrt{6} + 3)`
`= 5 - 5 + 2\sqrt{6}`
`= 2\sqrt{6}`
