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begin mathsize 14px style open parentheses x to the power of a over x to the power of b close parentheses to the power of a plus b end exponent times open parentheses x to the power of b over x to the power of c close parentheses to the power of b plus c end exponent times open parentheses x to the power of c over x to the power of a close parentheses to the power of c plus a end exponent equals end style 

  1. begin mathsize 14px style open parentheses x to the power of a over x to the power of b close parentheses to the power of c end style 

  2. begin mathsize 14px style open parentheses x to the power of b over x to the power of c close parentheses to the power of a end style 

  3. begin mathsize 14px style open parentheses x to the power of c over x to the power of a close parentheses to the power of b end style 

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begin mathsize 14px style open parentheses x to the power of a over x to the power of b close parentheses to the power of a plus b end exponent times open parentheses x to the power of b over x to the power of c close parentheses to the power of b plus c end exponent times open parentheses x to the power of c over x to the power of a close parentheses to the power of c plus a end exponent equals open parentheses x to the power of a open parentheses a plus b close parentheses end exponent over x to the power of b open parentheses a plus b close parentheses end exponent close parentheses times open parentheses x to the power of b open parentheses b plus c close parentheses end exponent over x to the power of c open parentheses b plus c close parentheses end exponent close parentheses times open parentheses x to the power of c open parentheses c plus a close parentheses end exponent over x to the power of a open parentheses c plus a close parentheses end exponent close parentheses equals open parentheses x to the power of a squared plus a b end exponent over x to the power of a b plus b squared end exponent close parentheses times open parentheses x to the power of b squared plus b c end exponent over x to the power of b c plus c squared end exponent close parentheses times open parentheses x to the power of c squared plus a c end exponent over x to the power of a c plus a squared end exponent close parentheses equals x to the power of open parentheses a squared plus a b close parentheses minus open parentheses a b plus b squared close parentheses end exponent times x to the power of open parentheses b squared plus b c close parentheses minus open parentheses b c plus c squared close parentheses end exponent times x to the power of open parentheses c squared plus a c close parentheses minus open parentheses a c plus a squared close parentheses end exponent equals x to the power of a squared minus b squared end exponent times x to the power of b squared minus c squared end exponent times x to the power of c squared minus a squared end exponent equals x to the power of a squared minus b squared plus b squared minus c squared plus c squared minus a squared end exponent equals x to the power of 0 equals 1 end style 

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