# Division

Algebra Level 5

${\displaystyle \left(\sum _{n=1}^{99}\sqrt{10+\sqrt{n}} \right)} \div { \displaystyle \left(\sum _{n=1}^{99}\sqrt{10-\sqrt{n}}\right) }$

If the expression above is equal to $$a+b\sqrt{c}$$ for integers $$a,b,c$$ with $$c$$ square-free, find $$a+b+c$$.

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