Question

先化简,再求值:1/x+1-1/x²-1÷x+1/x²-2x+1,其中x=√3-1

Answer 1

:1/x+1-1/x²-1÷x+1/x²-2x+1,其中x=√3-1
=1/(x+1)-1/(x+1)(x-1)×(x-1)²/(x+1)
=1/(x+1)-(x-1)/(x+1)²
=(x+1-x+1)/(x+1)²
=2/(x+1)²
=2/(√3-1+1)²
=2/3;

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Answer 2

1/(x+1)-1/(x²-1)÷(x+1)/(x²-2x+1)
=1/(x+1)-1/((x+1)(x-1))*(x-1)²/(x+1)
=1/(x+1)-(x-1)/(x+1)²
=(x+1)/(x+1)²-(x-1)/(x+1)²
=2/(x+1)²
=2/(√3-1+1)²
=2/3