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