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Question

Simplify the following expression:

1a+1b+c1a1b+c(1+b2+c2a22bc)(a+b+c)2

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Solution

1a+1b+c1a1b+c=a+b+cb+ca

1+b2+c2a22bc=b2+c2+2bca22bc=(a+b+c)(b+ca)2bc

1a+1b+c1a1b+c(1+b2+c2a22bc)(a+b+c)2=a+b+cb+ca×(a+b+c)(b+ca)2bc×1(a+b+c)2=12bc

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