'Bashing' Telescope.

Algebra Level 5

i=2104i5+10i4+16i3+14i24i4i8+4i7+2i68i57i4+4i3+4i2\large \displaystyle \sum_{i=2}^{10} \dfrac{4i^5 + 10i^4 + 16i^3 + 14i^2-4i - 4}{i^8 + 4i^7 + 2i^6 - 8i^5 - 7i^4 + 4i^3 + 4i^2}

If the above summation can be simplified to ab \dfrac{a}{b} where aa and bb are coprime positive integers . What is the value of a+ba+b?

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