Is it acceptable to omit 的 before a noun in degree complement, when the verb follows the noun?

Question

In the example sentence (according to Chinese grammar wiki):

你的菜做得很好。

你的字写得很漂亮。

你的中文说得很好。

In these cases, all use 的 before a noun, once it moves before the verb. The original sentence does not use 的 to modify the noun (e.g. 你做菜做得很好。).

But I feel I have also seen such sentences without 的 modification, for example:

你菜做得很好。

你字写得很漂亮。

你中文说得很好。

Or the sentence that made me determined to open this question:

凭着他的才能和经验，他在云南事情办得很顺利。

Maybe syllables are also taken in consideration here. 你中文说得很好 sounds more natural than the others, as those nouns are just one character.

So is it acceptable or not to omit 的 here? Or is it grammatically wrong but used commonly?

Answer 1

You cannot omit the possessive 的 in 你的菜, 你的字, 你的中文, if your comments are about 'your cooking', 'your writing' or 'your Chinese'

However, you can remove (not omit) '的' to change the topic from '你的~ (your~)' to '你 (you)'

[你的菜 (topic)] [做得很好(comment)] - "your cooking is cooked very well"

[你的字 (topic)] [写得很漂亮 (comment)] " your writing is written very beautifully"

[你的中文 (topic)] [说得很好 (comment)] "Your Chinese is spoken very well"

'你的菜', '你的字' and '你的中文' are the topics

~

[你 (topic)] [菜做得很好 (comment)] - "you cook very well"

[你 (topic)] [字写得很漂亮 (comment)] - "you write very beautifully"

[你 (topic)] [中文说得很好 (comment)] - "you speak Chinese very well"

'你' is the topics

~

'你做得很好', '你写得很漂亮' and '你说得很好' are basic [subject + verb] phrases

Answer 2

There's a nuance.

你菜做得很好 means generally your cooking is good.

Well, 你的菜做得很好, depending on contexts, could mean either generally your cooking is good or the speaker refers to those dishes cooked by you are good.

But in practice, there really isn't any difference and you can use them interchangeably.

This reminds me a similar omission in English: I go see your dog vs I go to see your dog.