Usuń niewymierność : 1) [latex] frac{2}{3- sqrt{5} } [/latex] 2) frac{12}{ sqrt{15} } 3) frac{3}{ sqrt{2-2} } 4) frac{ sqrt{2} }{3+ sqrt{2} } [/latex] Proszę o rozwiązanie, chodzi o usunięcie niewymierności :)

1) [latex]frac{2}{3- sqrt{5} }=frac{2(3+ sqrt{5})}{(3- sqrt{5})(3+sqrt{5}) }=frac{2(3+ sqrt{5})}{9-5}=frac{2(3+ sqrt{5})}{4}=frac{3+ sqrt{5}}{2}[/latex] 2) [latex]frac{12}{ sqrt{15} }=frac{12 sqrt{15} }{ sqrt{15} cdot sqrt{15} }=frac{12 sqrt{15} }{ 15 }=frac{4sqrt{15} }{ 5 }[/latex] 3) [latex]frac{3}{ sqrt{2}-2 }=frac{3(sqrt{2}+2)}{ (sqrt{2}-2 )(sqrt{2}+2)}=frac{3(sqrt{2}+6)}{2-4}=-frac{3(sqrt{2}+6)}{2}[/latex] 4) [latex]frac{ sqrt{2} }{3+ sqrt{2} }=frac{ sqrt{2}(3-sqrt{2}) }{(3+ sqrt{2})(3-sqrt{2}) }=frac{3 sqrt{2}-2}{9-2}=frac{3 sqrt{2}-2}{7}[/latex]