# When will the holidays come 1

Algebra Level 5

If $$1,\alpha_1,\alpha_2,\alpha_3,\alpha_4$$ are fifth roots of unity, and

$\displaystyle\sum_{i=1}^4 \dfrac{1}{2-\alpha_i}=\dfrac{a}{b}$

Where $$a$$ and $$b$$ are coprime integers then find $$a-b$$.

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