SOLUTION: Evaluate: (a-b)/ab + (b-c)/bc + (c-a)/ca

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Question 237247: Evaluate: (a-b)/ab + (b-c)/bc + (c-a)/ca
Answer by rapaljer(4551) About Me  (Show Source):
You can put this solution on YOUR website!
First find the LCD for the problem, which is abc


%28a-b%29%2F%28ab%29+%2B+%28b-c%29%2F%28bc%29+%2B+%28c-a%29%2F%28ca%29

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:
%28%28a-b%29%2F%28ab%29%29%2A%28c%2Fc%29+%2B+%28%28b-c%29%2F%28bc%29%29%2A%28a%2Fa%29+%2B+%28%28c-a%29%2F%28ca%29%29%2A%28b%2Fb%29

Now, multiply the numerators out, and place over the LCD, which is abc:
+%28c%28a-b%29+%2Ba%28b-c%29+%2Bb%28c-a%29%29%2F%28abc%29

%28ac-bc+%2Bab-ac+%2Bbc+-+ab%29%2F%28abc%29+

The entire numerator subtracts out, which leaves a numerator of 0.
0%2F%28abc%29
0.

VERY NICE PROBLEM!!!

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