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Let $c( a, b, c ) = \frac{a}{b} + \frac{b}{c} + \frac{c}{a}$. Compute $c(2, 12, 9)$.

 Jul 6, 2018
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\(c(\textcolor{red}{a},\textcolor{blue}{b},\textcolor{green}{c})= \frac{\textcolor{red}{a}}{\textcolor{blue}{b}}+ \frac{\textcolor{blue}{b}}{\textcolor{green}{c}}+ \frac{\textcolor{green}{c}}{\textcolor{red}{a}};\\ c(\textcolor{red}{2},\textcolor{blue}{12},\textcolor{green}{9})= \frac{\textcolor{red}{2}}{\textcolor{blue}{12}}+ \frac{\textcolor{blue}{12}}{\textcolor{green}{9}}+ \frac{\textcolor{green}{9}}{\textcolor{red}{2}}\) This shows the relationship of the input to the problem at hand. It is now necessary to convert all fractions to common denominators so that we can simplify the right-hand side. The LCM, in this case, is 36. 
\(c(a,b,c)=\frac{6}{36}+\frac{48}{36}+\frac{162}{36}\)  
\(c(a,b,c)=\frac{216}{36}=6\) That's quite a nice result, don't you think?
   
 Jul 7, 2018

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