3-2\sqrt{5}+2+3\sqrt{5}=5+\sqrt{5}
3-2\sqrt{5}-(2+3\sqrt{5})=3-2\sqrt{5}-2-3\sqrt{5}=1-5\sqrt{5}
(3-2\sqrt{5})*(2+3\sqrt{5})=3*2+3*3\sqrt{5}-2*2\sqrt{5}-2\sqrt{5}*3\sqrt{5}=6+9\sqrt{5}-4\sqrt{5}-2*3*5=6-30+5\sqrt{5}=-24+5\sqrt{5}
\frac{3-2\sqrt{5}}{3\sqrt{5}}=\frac{(3-2\sqrt{5})(2-3\sqrt{5})}{(2+3\sqrt{5})(2-3\sqrt{5})}=\frac{3*2-9\sqrt{5}-4\sqrt{5}+6*5}{2^2-(3\sqrt{5})^2}=\frac{36-13\sqrt{5}}{4-15}=\frac{36-13\sqrt{5}}{-11}=-\frac{36-13\sqrt{5}}{11}