SEAMO 2027 - Paper E - SET 08 - Self-study Question 11

Real numbers $a,b,c$ satisfy $\dfrac{ab}{a+b}=\dfrac13$, $\dfrac{bc}{b+c}=\dfrac14$ and $\dfrac{ca}{c+a}=\dfrac15$. Find $\dfrac{abc}{ab+bc+ca}$.