How did n2 / n lg n = n / n lg n?

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I recently stumbled on this equation

enter image description here

so how did $n^2 / n \lg n = n / n \lg n$ ?

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Read your image closer.

$\dfrac{n^2}{n\lg n}$ did not become $\dfrac{n}{n\lg n}$. It became $\dfrac{n}{\lg n}$, by dividing both numerator and denominator by $n$.