Question

化简分式x-（1/1-x）-（x^3-3x+1/x^2-1）,并求x=-1/3时该分式的值.

Answer 1

x-（1/1-x）-（x^3-3x+1/x^2-1）

＝x-(1/1-x)-{x(x^2-1)-2x+1}/x^2-1

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

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

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

=3x/x^2-1

=(3x-1/3 )/(-1/3)^2-1

=-1/(-8/9)

=9/8