2. If $a, b, c$ are real numbers such that $|a-b|=1,|b-c|=1,|c-a|=2$ and $a b c=60$, find the value of $\frac{a}{b c}+\frac{b}{c a}+\frac{c}{a b}-\frac{1}{a}-\frac{1}{b}-\frac{1}{c}$.
(A) $\frac{1}{30}$
(B) $\frac{1}{20}$
(C) $\frac{1}{10}$
(D) $\frac{1}{4}$
(E) None of the above
2. Answer: (B)
$$
\begin{aligned}
\frac{a}{b c}+\frac{b}{c a}+\frac{c}{a b}-\frac{1}{a}-\frac{1}{b}-\frac{1}{c} & =\frac{a^{2}+b^{2}+c^{2}-b c-c a-a b}{a b c} \\
& =\frac{\left(a^{2}-2 a b+b^{2}\right)+\left(b^{2}-2 b c+c^{2}\right)+\left(c^{2}-2 c a+a^{2}\right)}{2 a b c} \\
& =\frac{(a-b)^{2}+(b-c)^{2}+(c-a)^{2}}{2 a b c} \\
& =\frac{1^{2}+1^{2}+2^{2}}{120}=\frac{1}{20} .
\end{aligned}
$$