Đáp án: $B=1$
Giải thích các bước giải:
Ta có:
$\dfrac{ab}{a+b}=\dfrac{bc}{b+c}=\dfrac{ca}{c+a}$
$\to \dfrac{a+b}{ab}=\dfrac{b+c}{bc}=\dfrac{c+a}{ca}$
$\to \dfrac1a+\dfrac1b=\dfrac1b+\dfrac1c=\dfrac1c+\dfrac1a$
$\to \dfrac1a+\dfrac1b=\dfrac1b+\dfrac1c\to \dfrac1a=\dfrac1c\to a=c$
Và $\dfrac1b+\dfrac1c=\dfrac1c+\dfrac1a\to \dfrac1b=\dfrac1a\to a=b$
$\to a=b=c$
$\to B=1$