Докажите равенство ( 2V2+3)/(3-2V2)=17+12V2

(2v2+3)/(3-2v2)=(умножим и чеслитель и знаменатель на (3+2v2))=(6v2+8+9+6v2)/(9-8)=12v2+17 

[latex]frac{2sqrt{2}+3}{3-2sqrt{2}}=frac{(3+2sqrt{2})(3+2sqrt{2})}{(3-2sqrt{2})(3+2sqrt{2})}=frac{(3+2sqrt{2})^2}{3^2-(2sqrt{2})^2}=frac{3^2+2cdot3cdot2sqrt{2}+(2sqrt{2})^2}{9-2^2cdot(sqrt{2})^2}= \ =frac{9+12sqrt{2}+2^2(sqrt{2})^2}{9-2^2cdot(sqrt{2})^2}=frac{9+12sqrt{2}+4cdot2}{9-4cdot2}=frac{9+12sqrt{2}+8}{9-8}=frac{17+12sqrt{2}}{1}=17+12sqrt{2}[/latex]