SOLUTION: If x/(x²+1) = 2, then what is x²/(x⁴+1)

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Question 1206758: If x/(x²+1) = 2, then what is x²/(x⁴+1)
Answer by ikleyn(52754) About Me  (Show Source):
You can put this solution on YOUR website!
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If x/(x²+1) = 2, then what is x²/(x⁴+1)
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If  x%2F%28x%5E2%2B1%29 = 2, 


then  %28x%5E2%2B1%29%2Fx = 1%2F2;


then  %28x%5E4+%2B+2x%5E2+%2B+1%29%2Fx%5E2 = 1%2F4  (by squaring the preceding equality);


then  %28x%5E4+%2B+1%29%2Fx%5E2 + 2 = 1%2F4.


It implies

    %28x%5E4%2B1%29%2Fx%5E2 = 1%2F4-2 = -7%2F4.


Hence,  x%5E2%2F%28x%5E4%2B1%29 = -4%2F7.    ANSWER

Solved.

By the way, it means that x in the given/original equality is a complex number (not a real).