6. For the equation in terms of $x$
$$
\frac{1}{x^{2}-x}+\frac{k-5}{x^{2}+x}=\frac{k-1}{x^{2}-1}
$$

if it has an extraneous root $x=1$. Then the value of $k$ is ( ).
(A) 2
(B) 3
(C) 6
(D) 10
6. B.

Eliminating the denominator, we get
$$
x+1+(k-5)(x-1)=(k-1) x \text {. }
$$

Substituting $x=1$ yields $k=3$.