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(a + √b)/a√b = (a+√b)*√b / a√b*√b = (a√b + b)/ab
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(a + 2√(2a) + 2)/(√a + √2) = (a + 2√(2a) + 2)(√a - √2) / (√a + √2)(√a - √2) = (a√a + 2√(2a)√a + 2√a - a√2 - 2√(2a)√2 - 2√2) / (√a² - √2²) = (a√a + 2a√2 + 2√a - a√2 - 4√a - 2√2) / (a - 2) = (a√a + a√2 - 2√a - 2√2) / (a-2) = ( a(√a + √2) - 2(√a + √2))/(a - 2) = (a - 2)(√2 + √a)/(a - 2) = √a + √2
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6
(a + √b)/a√b = (a+√b)*√b / a√b*√b = (a√b + b)/ab
9
(a + 2√(2a) + 2)/(√a + √2) = (a + 2√(2a) + 2)(√a - √2) / (√a + √2)(√a - √2) = (a√a + 2√(2a)√a + 2√a - a√2 - 2√(2a)√2 - 2√2) / (√a² - √2²) = (a√a + 2a√2 + 2√a - a√2 - 4√a - 2√2) / (a - 2) = (a√a + a√2 - 2√a - 2√2) / (a-2) = ( a(√a + √2) - 2(√a + √2))/(a - 2) = (a - 2)(√2 + √a)/(a - 2) = √a + √2
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