How did they cancel out O-terms in this fraction? – cs.stackexchange.com

How did they cancel out O-terms in this fraction? – cs.stackexchange.com

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While reading a book about algorithms, I came across this derivation: $$ \frac{2a_0(2N) \ln(2N) + O(2N)}{2a_0N\ln N+O(N)} = \frac{2\ln(2N) + O(1)}{\ln N+O(1)} = 2 + O\left(\frac{1}{\log N}\right). $$ ...

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