а)
4/(√3 + 1) = 4*(√3 - 1) / (√3 + 1)(√3 - 1) = 4*(√3 - 1) / ((√3)² - 1²) =
= 4*(√3 - 1) / (3 - 1) = 4*(√3 - 1) / 2 = 2*(√3 - 1),
б)
1/(1 - √2) = 1*(1 + √2) / (1 + √2)(1 - √2) = (1 + √2) / (1² - (√2)²) =
= (1 + √2) / (1 - 2) = -(1 + √2) или -1 - √2,
а)
33/(7 - 3√3) = 33*(7 + 3√3) / (7 - 3√3)(7 + 3√3) =
= 33*(7 + 3√3) / (7² - (3√3)²) = 33*(7 + 3√3) / (49 - 27) =
= 33*(7 + 3√3) / (49 - 27) = 33*(7 + 3√3) / 22 = 1,5*(7 + 3√3),
б)
х/(√у + √z) = x*(√y - √z) / (√y + √z)(√y - √z) =
= x*(√y - √z) / ((√y)² - (√z)²) = x*(√y - √z) / (y -z)