Oh! Nice identity

Algebra Level 5

\( \dfrac{\sqrt{45+\sqrt{1}}+\sqrt{45+\sqrt{2}}+\sqrt{45+\sqrt{3}}+\ldots+\sqrt{45+\sqrt{2024}}}{\sqrt{45-\sqrt{1}}+\sqrt{45-\sqrt{2}}+\sqrt{45-\sqrt{3}}+\ldots+\sqrt{45-\sqrt{2024}}} = \ ? \)

Submit your answer to three decimal places.

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