先化简，再求值：x/x²-2x+1÷{（x+1/x²-1）+1}，其中x=根号2+1
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x/(x²-2x+1)÷[(x+1)/(x²-1)+1]
=x/(x-1)²÷[(x+1)+(x²-1)]/(x²-1)
=x/(x-1)²÷(x²+x)/[(x+1)(x-1)]
=x/(x-1)²÷[x(x+1)]/[(x+1)(x-1)]
=x/(x-1)²÷x/(x-1)
=x/(x-1)²·(x-1)/x
=1/(x-1)
=1/√2
=√2/2
=x/(x-1)²÷[(x+1)+(x²-1)]/(x²-1)
=x/(x-1)²÷(x²+x)/[(x+1)(x-1)]
=x/(x-1)²÷[x(x+1)]/[(x+1)(x-1)]
=x/(x-1)²÷x/(x-1)
=x/(x-1)²·(x-1)/x
=1/(x-1)
=1/√2
=√2/2
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原式=x/(x-1)²÷(x+1+x²-1)/(x²-1)
=x/(x-1)²*(x²-1)/(x+x²)
=x/(x-1)²*(x+1)(x-1)/x(x+1)
=x/(x-1)²*(x-1)/x
=1/(x-1)
=1/(√2+1-1)
=√2/2
=x/(x-1)²*(x²-1)/(x+x²)
=x/(x-1)²*(x+1)(x-1)/x(x+1)
=x/(x-1)²*(x-1)/x
=1/(x-1)
=1/(√2+1-1)
=√2/2
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x/x平方-2x+1÷{（x+1/x²-1）+1}，
=x/(x-1)平方 ÷{1/(x-1)+1}
=x/(x-1)平方 ÷x/(x-1)
=x/(x-1)平方 ×(x-1)/x
=1/(x-1)
x=根号2+1
所以
原式=1/(√2+1-1)=1/√2=√2/2
=x/(x-1)平方 ÷{1/(x-1)+1}
=x/(x-1)平方 ÷x/(x-1)
=x/(x-1)平方 ×(x-1)/x
=1/(x-1)
x=根号2+1
所以
原式=1/(√2+1-1)=1/√2=√2/2
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