$1 \cdot 68$ If $a, b$ and $c$ represent integers, the expressions $\sqrt{a+\frac{b}{c}}$ and $a \sqrt{\frac{b}{c}}$ are equal if and only if
(A) $a=b=c=1$.
(B) $a=b$ and $c=a=1$.
(C) $c=\frac{b\left(a^{2}-1\right)}{a}$.
(D) $a=b$ and $c$ is any value.
(E) $a=b$ and $c=a-1$.
(6th American High School Mathematics Examination, 1955)
[Solution] If $\sqrt{a+\frac{b}{c}}=a \sqrt{\frac{b}{c}}$, after simplification we have $(a c+b)=a^{2} b$, thus
$$
c=\frac{b\left(a^{2}-1\right)}{a} \text {. }
$$

Therefore, the answer is $(C)$.