Doprowadź wyrażenia do najprostszej postaci:   a) [latex]frac{12}{sqrt{6}}+frac{4sqrt{3}}{sqrt{2}}+frac{3sqrt{2}}{sqrt{3}}=[/latex] b) [latex]frac{12}{sqrt{10}}+frac{6}{sqrt{2}}-frac{15}{sqrt{5}}=[/latex]

a)[latex]frac{12}{sqrt{6}}+frac{4sqrt{3}sqrt{3}}{sqrt{6}}+frac{3sqrt{2}sqrt{2}}{sqrt{6}}=\frac{12}{sqrt6}}+frac{12}{sqrt{6}}+frac{6}{sqrt{6}}=frac{30}{sqrt{6}}=frac{30sqrt{6}}{sqrt{6}*sqrt{6}}=frac{30sqrt{6}}{6}=5sqrt{6}[/latex]   b)[latex]frac{12}{sqrt{10}}+frac{6}{sqrt{2}}-frac{15}{sqrt{5}}=[/latex] [latex]frac{12}{sqrt{10}}+frac{6sqrt{5}}{sqrt{10}}-frac{15sqrt{2}}{sqrt{10}}=\frac{12+6sqrt{5}-15sqrt{2}}{sqrt{10}}=\frac{12sqrt{10}+6sqrt{50}-15sqrt{20}}{10}=\frac{12sqrt{10}+6cdot5sqrt{2}-15cdot2sqrt{5}}{10}=\frac{12sqrt{10}+30sqrt{2}-30sqrt{5}}{10}=frac{6sqrt{10}}{5}+3sqrt{2}-3sqrt{5}[/latex]   Można jeszcze wyciągnąć 3 przed nawias: [latex]3(frac{2sqrt{10}}{5}}+sqrt{2}+sqrt{5})[/latex]