Answer:
Step-by-step explanation:
1 / (1 + 1/sqrt(2))
= 1 / (1 + 1/sqrt(2)) * sqrt(2)/sqrt(2)
= sqrt(2) / (sqrt(2) + 1)
= sqrt(2) / (sqrt(2) + 1) * (sqrt(2) - 1) / (sqrt(2) - 1)
= (sqrt(2) * (sqrt(2) - 1)) / ((sqrt(2) + 1) * (sqrt(2) - 1)) #1
= (2 - sqrt(2)) / (2 - 1) #2
= 2 - sqrt(2)
#1 : (a - b) * (a + b) = a^2 - b^2
#2 : sqrt(a) * sqrt(a) = a
