# 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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