What is the difference between the two sentences - the one with "the" and another without?

You write the best.

You write best.
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the second sentence is incorrect. because we use the in superlative sentences, you can't take out the from in this sentence.

by the way you must use the. for example; we are the best. i hope i could help you.

all the time if you use superlative you must use with the
I'm afraid I'll have to disagree... Have a look here: (the) + superlative

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but i have talked to my teacher who is from Chicago. He said that It was a rule and you couldn't break the rule.

and i know too, it is a rule if you don't want to speak accordingly rule, you can. but if you speak without the it isn't grammatically correct. of course, we don't speak grammatically all the time. but we should speak correct, shouldn't we?

so you must use the. without the like speaking street language. Emotion: smile
I found both examples in Cambridge:

Which evening would suit you best for the party? (best = superlative of well)
It's best (= It is wise) to get to the supermarket early. (best = superlative of good)

I guess you have to use "the" when "best" accompanies a noun, but you can leave it out when it doesn't.
yes i understand what you said. for example i'm the greatest. and it is best to go there and speak about their future.

you meant that, didn't you?
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Yes, I mean when it's used attributively, you can't leave out the "the". "I'm the greatest (singer on the earth). You can leave it out when it's used as a predicate, or if it has an adverbial value.
I have a couple of examples:

You write better after you have slept enough, your ideas are clear by then.

You write the best essays in this school.
I'm sorry, but "better" is not a superlative ... Emotion: sad
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