化简(3+√3)/[√2-√(2-√3)]
问题描述：
化简(3+√3)/[√2-√(2-√3)]
答
(3 + √3) / [√2 - √(2 - √3)] = (3 + √3) / {√2 - √[(√3 - 1)^2 / 2 ] } = (3 + √3) / {√2 - (√3 -1) * (√2) / 2} = (3 + √3) / {√2 - (√6 - √2) / 2} = (3 + √3) / {(3√2 - √6) / 2} = 2 * (3 + √3) / (3√2 -√6) = 2 * (3 +√3) * (3√2 + √6) / [(3√2 - √6) * (3√2 + √6)] = 2 * (9√2 + 3√6 + 3√6 + 3√2) / (18 - 6) = 2 * (12√2 + 6√6) / 12 = 2√2 + √6