What is #(sqrt(5+)sqrt(3))/(sqrt(3+)sqrt(3+)sqrt(5))-(sqrt(5-)sqrt(3))/(sqrt(3+)sqrt(3-)sqrt(5))#?

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Answer 1 · 2018-03-30T09:45:40

#2/7#

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))/((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.