Wzó: a²-b²=(a-b)(a+b) - różnica kwadratów. [latex]a) frac{5-2sqrt{5}}{-3sqrt{5}}*frac{sqrt{5}}{sqrt{5}}=frac{5*sqrt{5}-2sqrt{5}*sqrt{5}}{-3sqrt{5}*sqrt{5}}=frac{5sqrt{5}-2*5}{-3*5}=frac{10-5sqrt{5}}{15}=frac{2-sqrt{5}}{3}\ b) frac{3sqrt{2}-4,5}{sqrt{8}-3}*frac{sqrt{8}+3}{sqrt{8}+3}=frac{3sqrt{2}*sqrt{8}+3sqrt{2}*3-4,5sqrt{8}-4,5*3}{sqrt{8}^{2}-3^{2}}=\ =frac{3sqrt{16}+9sqrt{2}-4,5sqrt{4*2}-13,5}{8-9}=frac{3*4+9sqrt{2}-4,5*2sqrt{2}-13,5}{-1}=\ =-(12+9sqrt{2}-9sqrt{2}-13,5)=1,5[/latex]
a) [latex]= frac{(5-2sqrt{5})cdot sqrt{5}}{-3sqrt[5}cdot sqrt{5}} = frac{5sqrt{5}-10}{-15} = -frac{sqrt{5}-2}{3}[/latex] b)[latex]=frac{3sqrt{2}-4,5)(sqrt{8}+3)}{(sqrt{8}-3)(sqrt{8}+3)} = frac{12-9sqrt{2}+9sqrt{2}-13,5}{8-9} = frac{-1,5}{-1} = 1,5[/latex]
