3.10 The solutions to the equation $x^{2}+3 x+\frac{1}{x-1}=a+\frac{1}{x-1}$ and the solutions to the equation $x^{2}+$ $3 x=a$ are
(A) the same.
(B) not the same.
(C) uncertain whether the same or not, depending on the value of $a$.
(D) none of the above conclusions is correct.
(2nd "Jinyun Cup" Junior High School Mathematics Invitational, 1985)
[Solution] From $x^{2}+3 x=a$ i.e., $x^{2}+3 x-a=0$,
we get
$$
x=\frac{-3 \pm \sqrt{9+4 a}}{2} \text{. }
$$

If $x \neq 1$, i.e., $a \neq 4$, the solutions of the two equations in the problem are the same; if $a=4$, the two equations have different solutions (the first equation does not hold when $x=1$). Therefore, the answer is $(C)$.