Variant 7.8.2. Real numbers $a, b, c$ are such that

$$
\left\{\begin{array}{l}
\frac{a b}{a+b}=3 \\
\frac{b c}{b+c}=5 \\
\frac{c a}{c+a}=8
\end{array}\right.
$$

Find the value of the expression $\frac{a b c}{a b+b c+c a}$.
Answer: $\frac{240}{79}$.