Find

$t_n = \dfrac{n^5 + n^3}{n^4 + n^2 + 1}$ - 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.