\( t_n = \dfrac{n^5 + n^3}{n^4 + n^2 + 1}\) - This is the nth term of a sequence

If sum of its n terms can be expressed as \( S_{n} = a_n^2 + a + \dfrac{1}{b_n^2 + b}\)

Find \(\dfrac{a_n}{b_n} + a + b\)

Note - a and b are fractions expressed in the smallest ratio.

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