(2x^2)/(x^4 + 1) = ((2x^2) * (1/ (2x^2)) ) / ((x^4 + 1) * (1 / (2x^2))) = 1 / ( (x^2)/2 + 1/(2x^2))

and i ALWAYS mess up here, just to make sure if 1 / (b / c) then you get c / b right? if thats right then the next part is right too

= (2 / x^2) + 2x^2

thats as far as i can simplify it

edit: so typing it up neatly:

Code:

1
------
2x^2 2x^2 1 2
---------- *------------ = ------------------------ = ----------------- + 2x^2
x^4 + 1 1 x^2 1 x^2
------ ------- + -------
2x^2 2 2x^2