Algebraic expressions - simplifying

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Hi all,

I'm retaking the GRE soon and I keep making stupid algebra mistakes in my calculus problems so I'm going through a textbook from 1965 that is helpful but has me stumped on some problems. I hope someone can steer me in the right direction.

1/(a-b)(a-c) + 1/(c-a)(c-b) + 1/(b-a)(b-c)

Is there a way to simplify this? If I start multiplying out everything to get the LCD my final answer will be huge. Thanks in advance
 
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It shouldn't be too terrible. The obvious thing to note is that (b - a) = -(a - b), for example.
 
Write everything with a denominator of (a-b)(a-c)(b-c) and add the fractions.
 
basic advice: do not fear to write something down, just because you think it will be large and unmanageable. you have to plunge in without fear of what will come out. you have to get your hands dirty.
 

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