Can someone please explain why this is true?
$$ \exp\left(\ln(x) + \frac{\ln(x)}{x} + \frac1x + O(\frac{1}{x^2})\right) = x \left(1 + \frac{\ln(x)}{x} + \frac{1}{x} + O(\frac{\ln(x)^2}{x^2})\right) $$
I know the basics of taylor expansion and have and idea of big O notation, but still don't get it
Thank you