1. Among the following questions (or say problems)
(1) The equation $x^{2}+\frac{1}{x-1}=1+\frac{1}{x-1}$ is a one-variable quadratic equation;
(3) Extend line $A B$ to $C$;
(1) Simplifying $a \sqrt{-\frac{1}{a}}$ yields $\sqrt{-a}$. The number of correct statements is ( .
(A) 1
(B) 2
(C) 3
(D) 4
$-.1 .(\mathrm{C})$.
$x^{2}+\frac{1}{x-1}=1+\frac{1}{x-1}$ is a fractional equation; an equilateral triangle is of course an isosceles triangle; a ray can only be extended in the reverse direction; for $a \sqrt{-\frac{1}{a}}$ to be meaningful, then $a<0$, thus, $a \sqrt{-\frac{1}{a}}=$ $-\sqrt{-a}$. Therefore, the answer is (C).