Question 1007707
4x
_______
x4 + 4x2 + 4       = 0


The equation looks like  (4x)/(x^4+4x^2)+4=0

rendered as {{{(4x)/(x^4+4x^2)+4=0}}}.


{{{4x/(x^4+4x^2)+4(x^4+4x^2)/(x^4+4x^2)=0}}}
{{{(4x+4(x^4+4x^2))/(x^4+4x^2)=0}}}
And the numerator is now what is important to equate to 0.


{{{4x+4x^4+16x^2=0}}}
{{{4x^4+16x^2+4x=0}}}
{{{x^4+4x^2+x=0}}}
{{{x(x^3+4x+1)=0}}}


The degree three factor has no apparent rational roots, as checked with Rational
Roots Theorem and synthetic division.  There is a root of 0 for the factor x.


The rational term in the original equation can be negative.  {{{x<>0}}} because that value will make the
denominator become 0, not allowed.


<s>NO SOLUTION</s>

A graphing program will show a root, not rational, near {{{-0.2462}}}.