Question 237247
First find the LCD for the problem, which is {{{abc}}}



{{{(a-b)/(ab) + (b-c)/(bc) + (c-a)/(ca)}}}


In the first fraction, you have a denominator of (ab), so you need to multiply by c/c.  In the second fraction, you must multiply by a/a, and the third fraction multiply by b/b:

{{{((a-b)/(ab))*(c/c) + ((b-c)/(bc))*(a/a) + ((c-a)/(ca))*(b/b)}}}


Now, multiply the numerators out, and place over the LCD, which is {{{abc}}}:
{{{ (c(a-b) +a(b-c) +b(c-a))/(abc)}}}


{{{(ac-bc +ab-ac +bc - ab)/(abc) }}}


The entire numerator subtracts out, which  leaves a numerator of 0.  
{{{0/(abc)}}}
{{{0}}}.


VERY NICE PROBLEM!!!  


Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus