Question

Show that `(sqrt5 + sqrt3)/(sqrt5 - sqrt3) - (sqrt5 - sqrt3)/(sqrt5 + sqrt3) = 2 sqrt15`

Answer 1

LHS `= (sqrt5 + sqrt3)/(sqrt5 - sqrt3) - (sqrt5 -sqrt3)/(sqrt5 + sqrt3) = ((sqrt5 + sqrt3)^(2) - (sqrt5 - sqrt3)^(2))/((sqrt5 - sqrt3) (sqrt5 + sqrt3))`
`= (4.sqrt5.sqrt3)/((sqrt5)^(2) - (sqrt3)^(2)) = (4 sqrt15)/(5 -3) = (4sqrt15)/(2) = 2sqrt15`= RHS.
`:. (sqrt5 + sqrt3)/(sqrt5 - sqrt3) - (sqrt5 - sqrt3)/(sqrt5 + sqrt3) = 2 sqrt15`