(2+√3+√5)/(2+√3-√5)=
(2+√3+√5)2/([(2+√3)2-5)]]=
(4+4√3+3+2√5(2+√3)+5)/(4+4√3+3-5)=
(12+4√3+4√5+2√15)/(2+4√3)=
(6+2√3+2√5+√15)/(1+2√3)=
(6+2√3+2√5+√15)(1-2√3)/(1-12)=
(6+2√3+2√5+√15-12√3-12-4√15-6√5)/-11=
(-6-10√3-4√5-3√15)/-11=
(6+10√3+4√5+3√15)/11=(6/11)+(10/11)√3+(4/11)√5+(3/11)√15.