Variant 7.8.3. Real numbers $a, b, c$ are such that

$$
\left\{\begin{array}{l}
\frac{a b}{a+b}=2 \\
\frac{b c}{b+c}=5 \\
\frac{c a}{c+a}=7
\end{array}\right.
$$

Find the value of the expression $\frac{a b c}{a b+b c+c a}$.
Answer: $\frac{140}{59}$.