In several slides, I found the asymptotic property called additivity as follows:
If $f = \Theta(h)$ and $g = O(h)$ then $f+g = \Theta(h)$.
Below a snapshot from one of this resources is shown:
I understand that if $ f = \Theta(h)$ and $g = \Theta(h)$ then $f+g = \Theta(h)$.
But I can not figure out the proof for the property in the slide. Also I couldn't find a textbook that explains it. I wonder if it is a typo. If not would you please help to explain it?
Thank you.