Plus and Minus Makes All the Differences

Evaluate

\[\frac{(10!+9!)(8!+7!)(6!+5!)(4!+3!)(2!+1!)}{(10!-9!)(8!-7!)(6!-5!)(4!-3!)(2!-1!)} . \]

Hint: You don't need to multiply out all the factorials!

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