a=1+√2
b=1-√2
(1/(a-b) - 1(/a+b)) ÷ (b/(a²-2ab+b²))
= ((a+b)-(a-b) / ((a+b)(a-b) * (a²-2ab+b²) / b
= 2b / ((a+b)(a-b) * (a-b)^2 / b
= 2(a-b) / (a+b)
= 2 {(1+√2)-(1-√2)} / ((1+√2)+(1-√2)}
= 4√2 /2
= 2√2
a=1+√2
b=1-√2
(1/(a-b) - 1(/a+b)) ÷ (b/(a²-2ab+b²))
= ((a+b)-(a-b) / ((a+b)(a-b) * (a²-2ab+b²) / b
= 2b / ((a+b)(a-b) * (a-b)^2 / b
= 2(a-b) / (a+b)
= 2 {(1+√2)-(1-√2)} / ((1+√2)+(1-√2)}
= 4√2 /2
= 2√2