Question

先化简代数式再求值(3/x+1 - x+1)÷x²-2x/x+1,其中x满足方程x/x-1+1/x=1

Answer 1

=[3/(x+1)-(x-1)]÷(x²-2x)/(x+1)

=[3/(x+1)-(x-1)(x+1)/(x+1)]÷x(x-2)/(x+1)

=[3-(x+1)(x-1)]/(x+1)÷x(x-2)/(x+1)

=[3-x²+1)]/(x+1)÷x(x-2)/(x+1)

=(4-x²)/(x+1)/(x+1)÷x(x-2)/(x+1)

=(2+x)(2-x)/(x+1)x(x-2)/(x+1)

=-(x+2)(x-2)/(x+1)*(x+1)/x(x-2)

=-(x+2)/x

x/(x-1) + 1/x = 1

(x² + x-1) / x(x-1)=1

x² + x-1 = x(x-1)

x² + x-1 = x² -x

2x=1

x = 1/2

(3/x+1 - x+1)÷x²-2x/x+1

=-(x+2)/x

=-(1/2+2)÷1/2

=-5/2*2

=-5