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Can the $\ce{HO}$ bond be written as $\ce{OH}$ and still be correct?

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They mean the same thing. If the OH group on the left were written as OH, it would look like there was a carbon-hydrogen bond. By inverting the order, it makes it clear that the oxygen is bonded to the carbon and the hydrogen is bonded to the oxygen. $\ce{NH2}$ might also be written as $\ce{H2N}$ in a structure drawing if a bond was coming from the right, but the functional group is the same in both cases—the group is connected to the rest of the molecule by the nitrogen atom.

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