Question 1206758
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If x/(x²+1) = 2, then what is x²/(x⁴+1)
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<pre>
If  {{{x/(x^2+1)}}} = 2, 


then  {{{(x^2+1)/x}}} = {{{1/2}}};


then  {{{(x^4 + 2x^2 + 1)/x^2}}} = {{{1/4}}}  (by squaring the preceding equality);


then  {{{(x^4 + 1)/x^2}}} + 2 = {{{1/4}}}.


It implies

    {{{(x^4+1)/x^2}}} = {{{1/4-2}}} = {{{-7/4}}}.


Hence,  {{{x^2/(x^4+1)}}} = {{{-4/7}}}.    <U>ANSWER</U>
</pre>

Solved.


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