# The nested radicals are back for 2016!

Algebra Level 5

$\displaystyle \frac{\displaystyle\sum_{x=1}^{2016} \sqrt{\left[x^{2} + x + 1 \right]+\sqrt{\left[x^{2} + x + 1\right]-\sqrt{\left[x^{2} + x + 1 \right]+\sqrt{\left[x^{2} + x + 1 \right]-\cdots}}}}}{\displaystyle \sum_{x=1}^{2016} \sqrt{\left[x^{2} + x + 1 \right]-\sqrt{\left[x^{2} + x + 1\right]+\sqrt{\left[x^{2} + x + 1 \right]-\sqrt{\left[x^{2} + x + 1 \right]+\cdots}}}}}$ If the value of the expression above can be represented in the form $$\dfrac{a}{b}$$, where $$a$$ and $$b$$ are coprime integers, find $$b-a$$.

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