当x为何值时,分式x^2-1/x^2-x的值为-1?

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当x为何值时,分式x^2-1/x^2-x的值为-1?当x为何值时,分式x^2-1/x^2-x的值为-1?当x为何值时,分式x^2-1/x^2-x的值为-1?x^2-1/x^2-x=-1x^2-1=-1

当x为何值时,分式x^2-1/x^2-x的值为-1?
当x为何值时,分式x^2-1/x^2-x的值为-1?

当x为何值时,分式x^2-1/x^2-x的值为-1?
x^2-1/x^2-x=-1
x^2-1=-1*(x^2-x)
(x+1)(x-1)+x(x-1)=0
(x-1)(x+1+x)=0
分母x^2-x=x(x-1)≠0
则x-1≠0
‘所以x+1+x=0
x=-1/2

-1/2

(x^2 - 1) / (x(x-1)) = -1 => x≠1& x≠0
x^2 - 1 = -x^2 + x
2x^2-x-1 = 0 => (x-1)(2x+1) = 0 => x1 = 1 or x2 = 1/2
∵ x≠1& x≠0
∴x = 1/2