Podeu començar racionalitzant:
# (sqrt (1 + x) + sqrt (1-x)) / (sqrt (1 + x) -sqrt (1-x)) × (sqrt (1 + x) + sqrt (1-x)) / ((sqrt (1 + x) + sqrt (1-x)) =
# = (sqrt (1 + x) + sqrt (1-x)) ^ 2 / (2x) = #
# = ((1 + x) + 2sqrt (1 + x) sqrt (1-x) + (1-x)) / (2x) = #
# = (2 + 2sqrt (1-x ^ 2)) / (2x) = #
# = (1 + sqrt (1-x ^ 2)) / (x) = #
Substitució: # x = sqrt (3) / 2 # obtens:
# = (1 + sqrt (1- 3/4)) / (sqrt (3) / 2) = (1 + 1/2) * (2 / sqrt (3)) = #
# = 3/2 * 2 / sqrt (3) = 3 / sqrt (3) = 3 / sqrt (3) * sqrt (3) / sqrt (3) = sqrt (3) #
Espero que sigui el que necessiteu!:-)
