c) 1/(6+V2) * (6-V2)/(6-V2) = (6-V2)/(36-2) = (6-V2)/34 d) 2V2/(V5+4) *(V5-4)/(V5-4) = 2V2(V5-4)/(5-16) = (2V10-8V2)/(-11) = -2(V10-4V2)/11 e) 2/(4-3V2) *(4+3V2)/(4+3V2) = 2(4+3V2)/(16-18) = 2(4+3V2)/(-2) = -(4+3V2) f) (2V3-1)/(2V3+2) *(2V3-2)/(2V3-2) = (2V3-1)(2V3-2)/(12-4) = (12-4V3-2V3+2)/8 = =(14-6V3)/8 = 2/8 *(7-3V3) = (7-3V3)/4 g) 1/(V3-V2) *(V3+V2)/(V3+V2) = (V3+V2)/(3-2) = V3+V2 h) V3/(V5+V3) * (V5-V3)/(V5-V3) = V3(V5-V3)/(5-3) = (V15-3)/(5-3) = (V15-3)/2
[latex]c) frac{1}{6+sqrt{2}}=frac{1}{6+sqrt{2}} imesfrac{6-sqrt{2}}{6-sqrt{2}}=frac{6-sqrt{2}}{(36-2)}=frac{3}{17}-frac{sqrt{2}}{34}[/latex] d)[latex]frac{2sqrt{2}}{sqrt{5}+4} imesfrac{sqrt{5}-4}{sqrt{5}-4}=frac{2sqrt{10}-8sqrt{2}}{5-16}=frac{2sqrt{10}-8sqrt{2}}{-11}[/latex] e)[latex]frac{2}{4-3sqrt{2}} imesfrac{4+3sqrt{2}}{{4+3sqrt{2}}}=frac{8+6sqrt{2}}{16-18}=-4-3sqrt{2}[/latex] f)[latex]frac{2sqrt{3}-1}{2sqrt{3}+2} imesfrac{2sqrt{3}-2}{2sqrt{3}-2}=frac{12-2sqrt{3}-4sqrt{3}+2}{12-4}=frac{14-6sqrt{3}}{8}[/latex] g)[latex]frac{1}{sqrt{3}-sqrt{2}} imesfrac{sqrt{3}+sqrt{2}}{sqrt{3}+sqrt{2}}=frac{sqrt{3}+sqrt{2}}{1}[/latex] h)[latex]frac{sqrt{3}}{sqrt{5}+sqrt{2}} imesfrac{sqrt{5}-sqrt{2}}{sqrt{5}-sqrt{2}}=frac{sqrt{15}-sqrt{6}}{3}[/latex]
