We take ,
#A=(sqrt5+sqrt3)/(sqrt3+sqrt3+sqrt5)-(sqrt5-sqrt3)/(sqrt3+sqrt3-sqrt5)#
#=(sqrt5+sqrt3)/(2sqrt3+sqrt5)-(sqrt5-sqrt3)/(2sqrt3-sqrt5)#
#=(sqrt5+sqrt3)/(2sqrt3+sqrt5)-(sqrt5-sqrt3)/(2sqrt3-sqrt5)#
#=((sqrt5+sqrt3)(2sqrt3-sqrt5)-(sqrt5-sqrt3)
(2sqrt3+sqrt5))/((2sqrt3+sqrt5)(2sqrt3-sqrt5)#
#=((2sqrt15-5+2*3-sqrt15)-(2sqrt15+5-2*3-sqrt15))/((2sqrt3)^2-
(sqrt5)^2)#
#=(cancel(2sqrt15)-5+2*3cancel(-sqrt15)-
cancel(2sqrt15)-5+2*3+cancel(sqrt15))/(12-5)#
#=(-10+12)/7#
#=2/7#
Note that, if in the denominators are
#(sqrt3+sqrt(3+sqrt5)) and
(sqrt3+sqrt(3-sqrt5)) #
then the answer will be change.