من میدانم که امروز خسته ای، اما اگر بخواهی میتوانیم با هم درس بخوانیم.

That’s true: Persian often omits subject pronouns because the verb ending already shows the person.

So می‌دانم already means I know, and the sentence could naturally begin as:

می‌دانم که...

Adding من makes the subject a little more explicit. It can sound:

• slightly more personal,
• slightly more emphatic,
• or just stylistic.

So both are possible:

• من می‌دانم که امروز خسته‌ای...
• می‌دانم که امروز خسته‌ای...

Both mean the same thing here.

که often means that and introduces a clause after verbs like know, say, think, etc.

So:

• می‌دانم = I know
• که امروز خسته‌ای = that you are tired today

This is very similar to English I know that...

In Persian, که is very common in this kind of sentence, and it usually sounds natural to include it.

خسته‌ای means you are tired, but grammatically it is made from:

• خسته = tired
• ای = you are (2nd person singular form of to be)

So literally it is something like:

• tired + are

This is a very common Persian pattern with adjectives:

• خوبی = you are well
• آماده‌ای = you are ready
• خسته‌ای = you are tired

So خسته‌ای is not just a plain adjective by itself; it includes the copula ending.

The more standard spelling is خسته‌ای with a half-space (technically a zero-width non-joiner) before ای.

Similarly, standard modern spelling usually writes:

• می‌دانم rather than میدانم
• می‌توانیم rather than میتوانیم
• خسته‌ای rather than خسته ای

You will often see the version without the half-space in casual typing, messages, older materials, or when people do not use Persian keyboard conventions carefully. Both are understandable, but the version with the half-space is considered better standard writing.

After اگر (if), Persian often uses a form that looks like the subjunctive/present stem with ب.

Here:

• خواستن = to want
• خواهی = you want / you will want depending on context
• بخواهی = if you want / should you want

So:

• اگر بخواهی = if you want

This is a very common pattern in Persian conditional sentences.

بخواهی comes from the verb خواستن (to want).

Breakdown:

• present stem: خواه-
• subjunctive marker: بـ
• 2nd person singular ending: ـی

So:

• ب + خواه + ی = بخواهی

This gives you want / if you want / that you want depending on context.
In this sentence, because of اگر, it means if you want.

Good question. The sentence says:

• اگر بخواهی = if you want
• می‌توانیم = we can

So the subject changes:

• you in بخواهی
• we in می‌توانیم

This is perfectly natural. The meaning is:

I know you’re tired today, but if you want, we can study together.

So the speaker is saying:
It depends on you, but both of us can do it.

The ending ـیم in می‌توانیم shows we.

Yes. توانستن literally means to be able.

So:

• می‌توانیم literally = we are able
• natural English = we can

This is just like how English often prefers can instead of are able to.

Breakdown:

• می‌ = imperfective/present marker
• توان = verb stem related to ability
• ـیم = we

So می‌توانیم = we can / we are able to

با هم means together or more literally with each other / with one another.

Breakdown:

• با = with
• هم = each other / together / jointly, depending on context

In this sentence:

• با هم درس بخوانیم = let’s study together / we can study together

Yes, با هم is a very common and natural way to say together in Persian.

Yes, خواندن often means to read, but in Persian درس خواندن is a common expression meaning to study.

So:

• درس = lesson
• خواندن = to read
• درس خواندن = to study

Literally, it may feel like to read lessons, but idiomatically it means to study.

This is a useful thing to remember: Persian often uses noun + light verb / common verb combinations whose overall meaning is not fully literal in English.

Yes. بخوانیم is a subjunctive form of خواندن.

Breakdown:

• present stem: خوان
• subjunctive marker: بـ
• ـیم = we

So:

• بخوانیم = that we read / that we study / let us study, depending on context

In this sentence, after می‌توانیم, Persian commonly uses this form:

• می‌توانیم ... بخوانیم = we can study

So even though English uses study, Persian uses the subjunctive form بخوانیم after can/be able.

Persian usually prefers Subject – Object/Complements – Verb, so the verb often comes near the end of its clause.

A rough structure here is:

• من می‌دانم
• که امروز خسته‌ای
• اما اگر بخواهی
• می‌توانیم با هم درس بخوانیم

If we label the last part:

• می‌توانیم = we can
• با هم = together
• درس بخوانیم = study

Even though می‌توانیم appears earlier, the main lexical action بخوانیم still comes at the end of the clause, which is very Persian-like.

A careful pronunciation would be approximately:

man midânam ke emruz khaste-i, ammâ age bekhâhi mitavânim bâ ham dars bekhânim

A few notes:

• اگر is often pronounced more casually as اَگه / age
• خسته‌ای is pronounced like khaste-i
• می‌دانم sounds like midânam
• می‌توانیم sounds like mitavânim

In everyday speech, pronunciation may be a little smoother and less formal than the fully careful version.

Yes. A more conversational version might be something like:

می‌دونم که امروز خسته‌ای، ولی اگه بخوای می‌تونیم با هم درس بخونیم.

Common colloquial changes:

• می‌دانم → می‌دونم
• اما → ولی
• اگر → اگه
• بخواهی → بخوای
• می‌توانیم → می‌تونیم
• بخوانیم → بخونیم

This is very natural in spoken Persian. The original sentence is perfectly correct and a bit more standard/written.

Yes. اما means but, but in everyday speech many speakers prefer ولی.

So both are correct:

• اما اگر بخواهی...
• ولی اگر بخواهی...

In general:

• اما can feel a bit more formal or written
• ولی is very common in conversation

If you want to read and write standard Persian well, yes, it’s worth learning.

The half-space is especially common with:

• the prefix می‌
• some suffixes like ـای in خسته‌ای

So standard forms here are:

• می‌دانم
• خسته‌ای
• می‌توانیم

However, don’t panic if you see:

• میدانم
• خسته ای
• میتوانیم

Those are extremely common in informal typing, and learners should be able to recognize both.