x/(x^2+x+1)=m
1/(x+1+1/x)=m
x+1+1/x=1/m
x+1/x=1/m -1=(1-m)/m
x^2/(x^4+x^2+1)
=1/(x^2+1+1/x^2)
=1/[(x+1/x)^2-1]
=1/[(1-m)^2/m^2-1]
=m^2/(1-2m)