Don't they look equal?

Algebra Level 3

A=99999+1991000+1B=991000+1991001+1A = \dfrac{99^{999} + 1}{99^{1000}+1} \hspace{1.5cm} B = \dfrac{99^{1000}+1}{99^{1001}+1}

Which of AA and BB is greater?

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