1951 AMC 12 Question 44
AMC12 · 1951 AMC 12
If $\dfrac{xy}{x+y}=a,$ $\dfrac{xz}{x+z}=b,$ and $\dfrac{yz}{y+z}=c,$ where $a,$ $b,$ $c$ are other than zero, then $x$ equals:
$\dfrac{abc}{ab+ac+bc}$
$\dfrac{2abc}{ab+bc+ac}$
$\dfrac{2abc}{ab+ac-bc}$
$\dfrac{2abc}{ab+bc-ac}$
$\dfrac{2abc}{ac+bc-ab}$