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Question

fraction numerator 1 over denominator x to the power of 4 plus 1 end fraction equals

  1. fraction numerator x plus square root of 2 over denominator 2 square root of 2 open parentheses x squared plus square root of 2 x minus 1 close parentheses end fraction plus fraction numerator square root of 2 minus x over denominator 2 square root of 2 open parentheses x squared plus square root of 2 x minus 1 close parentheses end fraction
  2. fraction numerator x plus square root of 2 over denominator 2 square root of 2 open parentheses x squared plus square root of 2 x plus 1 close parentheses end fraction plus fraction numerator square root of 2 minus x over denominator 2 square root of 2 open parentheses x squared minus square root of 2 x plus 1 close parentheses end fraction
  3. fraction numerator x plus square root of 2 over denominator 2 square root of 2 open parentheses x squared plus square root of 2 x minus 1 close parentheses end fraction plus fraction numerator square root of 2 minus x over denominator 2 square root of 2 open parentheses x squared minus square root of 2 x plus 1 close parentheses end fraction
  4. fraction numerator x plus square root of 2 over denominator 2 square root of 2 open parentheses x squared minus square root of 2 x plus 1 close parentheses end fraction plus fraction numerator square root of 2 minus x over denominator 2 square root of 2 open parentheses x squared minus square root of 2 x plus 1 close parentheses end fraction

The correct answer is: fraction numerator x plus square root of 2 over denominator 2 square root of 2 open parentheses x squared plus square root of 2 x plus 1 close parentheses end fraction plus fraction numerator square root of 2 minus x over denominator 2 square root of 2 open parentheses x squared minus square root of 2 x plus 1 close parentheses end fraction

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