Proszę o pomoc w zadaniu z usuwania niewymiernosci z mianownika najlepiej z wyjaśnieniem bo kompletnie nie rozumiem

a) [latex]a = cfrac{1}{sqrt{3} - 1} = cfrac{1}{sqrt{3} - 1} cdot cfrac{sqrt{3} + 1}{sqrt{3} + 1} = cfrac{1(sqrt{3} + 1)}{(sqrt{3} - 1)(sqrt{3} + 1)} = cfrac{sqrt{3} + 1}{(sqrt{3})^2 - 1^2} = cfrac{sqrt{3} + 1}{2}[/latex] [latex]b = cfrac{2}{sqrt{5} - 1} - cfrac{2}{sqrt{5} + 1} = cfrac{2(sqrt{5} + 1)}{(sqrt{5} -1)(sqrt{5} + 1)} - cfrac{2(sqrt{5} - 1)}{(sqrt{5} - 1)(sqrt{5} + 1)} = cfrac{2sqrt{5} + 2 - 2sqrt{5} + 2}{(sqrt{5})^2 - 1^2} = cfrac{4}{4} = 1[/latex] [latex]a - b = cfrac{sqrt{3} + 1}{2} - 1 = cfrac{sqrt{3} + 1 - 2}{2} = cfrac{sqrt{3} - 1}{2} > 0[/latex] [latex]a - b > 0[/latex] to [latex]a > b[/latex] b) [latex]a = cfrac{(sqrt{2} - 3)^2}{2} = cfrac{(sqrt{2})^2 - 2 cdot sqrt{2} cdot 3 + 3^2}{2} = cfrac{2 - 6sqrt{2} + 9}{2} = cfrac{11 - 6sqrt{2}}{2}[/latex] [latex]b = cfrac{1}{2 - sqrt{2}} = cfrac{1}{2 - sqrt{2}} cdot cfrac{2 + sqrt{2}}{2 + sqrt{2}} = cfrac{2 + sqrt{2}}{2^2 - (sqrt{2})^2} = cfrac{2 + sqrt{2}}{2}[/latex] [latex]a - b = cfrac{11 - 6sqrt{2}}{2} - cfrac{2 + sqrt{2}}{2} = cfrac{11 - 6sqrt{2} - 2 - sqrt{2}}{2} = cfrac{9 - 7sqrt{2}}{2} < 0[/latex] [latex]a - b < 0[/latex] to [latex]a < b[/latex]