Question (x^4 + 3x^2 + 1) / (1/x^3 + 1/x)

ans: ((4x^3 + 6x)(1/x^3 + 1/x) - (x^4 + 3x^2 + 1)(-3/x^4 - 1/x^2))/(1/x^3 + 1/x)^2

Now, lets simplify:

ans = ((4 + 6 + 4x^2 + 6/x^2) - (-3 -3 - x^2 - 9/x^2 - 3/x^4 - 1/x^2))/(1/x^6+2/x^4+1/x^2)
= (16 + 5x^2 + 16/x^2 + 3/x^4)/(1/x^6 + 2/x^4 + 1/x^2)

multiply by x^6:

= (3x^2 + 16x^4 + 16x^6 + 5x^8)/(x^2 + 1)^2

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