Answer
(2 - √2) / (1 + √2)^2 = (2 - √2) / (1 + 2√2 + 2) = (2 - √2) / (3 + 2 √2)
(2 - √2) / (3 + 2 √2) * (3 - 2 √2) / (3 - 2 √2) multiply by 1
= (6 - 7√2 + 4) / (9 - 8) since (a - b) ( a + b) = a^2 - b^2
= 10 -7√ 2
Check:
(2 - √2) / (1 + √2)^2 = (2 - 1.414) / (2.414)^2 = .100
10 - 7√2 = 10 - 7 * 1.414 = .102