(2+√2)÷ (2-√2)－1÷(√2-1)

(2+√2)÷ (2-√2)－1÷(√2-1)
=(2+√2)(2+√2)÷[(2-√2)(2+√2)]－1*(√2+1)÷[(√2-1)(√2+1)]
=(4+2+4√2)÷2-(√2+1)
=3+2√2-√2-1
=2+√2

（2+√2)÷ (2-√2)－1÷(√2-1)
=（2+√2)^2÷ (2-√2)（2+√2)－(√2+1)÷(√2-1)(√2+1)
=(4+4√2+2)÷(4-2)-(√2+1)÷(2-1)
=3+2√2-(√2+1)
=√2+2

(2+√2)÷ (2-√2)－1÷(√2-1)
=(2+√2)^2÷[(2-√2)(2+√2)]-(√2+1)÷[(√2-1)(√2+1)]
=(4+4√2+2)÷(4-2)-(√2+1)÷(2-1)
=(6+4√2)÷2-(√2+1)
=3+2√2-√2-1
=2+√2

原式=(2+√2)÷ (2-√2)-(1+√2)
=(2+√2-√2)÷(2-√2)
=(2+√2)(2-√2)÷(2-√2)
=(2+√2)

原式=
=((2+√2)^2/(2-√2)(2+√2))-((√2+1)/(√2+1)(√2-1))
=((6+4√2)/2)-((√2+1)/(1))
=3+2√2-√2-1
=2+√2

分母有理化，两边的分母分别乘以2+√2和1+√2即可得到3+√2-(1+√2)=2-√2,所以答案为2-√2