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Don't they look equal?

Algebra Level 3

\[A = \dfrac{99^{999} + 1}{99^{1000}+1} \hspace{1.5cm} B = \dfrac{99^{1000}+1}{99^{1001}+1} \]

Which of \(A\) and \(B\) is greater?

Both are equal \[B\] \[A\]

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by Anuj Shikarkhane

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