Question

(2((√3)+(√5)))/((√5)-(√3))-2√15

Answer 1

$frac{2(sqrt3+sqrt5)}{sqrt5-sqrt3} -2sqrt{15}= frac{2(sqrt3+sqrt5)(sqrt5+sqrt3)}{(sqrt5-sqrt3)(sqrt5+sqrt3)} -2sqrt{15}=\\= frac{2(sqrt5+sqrt3)^2}{5-3} -2sqrt{15}= frac{2(5+2sqrt5cdot sqrt3+3)}{2} -2sqrt{15}=\\=8+2sqrt{15}-2sqrt{15}=8$