اليوم أنا مشغول في العمل، وصديقتي مشغولة في الجامعة.

In Modern Standard Arabic, the verb to be is usually not stated in the present tense.

So: أنا مشغول literally looks like I busy, but it means I am busy.

The same happens in: صديقتي مشغولة = My friend is busy

Arabic does use forms of to be in the past and future, but in the present, a nominal sentence like this normally just puts the subject and the predicate next to each other.

اليوم means today, and here it functions as a time expression.

Putting it at the beginning gives a slight emphasis to today, as in: Today, I’m busy at work...

You could also place it later, for example: أنا مشغول في العمل اليوم This is also natural, but the emphasis is slightly different.

Here أنا is the subject of the first clause, so it is important.

In a sentence like أنا مشغول, the adjective مشغول by itself does not tell you who is busy. Arabic needs something to show the subject, and here that is أنا.

In conversation, Arabic sometimes drops things that are understood from context, but in clear, standard written Arabic, أنا is the normal and safe choice here.

Because صديقتي is already the subject.

The structure is: صديقتي = subject
مشغولة = predicate

So صديقتي مشغولة already means my friend is busy. You do not need هي because the noun itself is doing the job of the subject.

In other words:

• أنا مشغول = pronoun subject + predicate
• صديقتي مشغولة = noun subject + predicate

Because Arabic adjectives must agree with the person or thing they describe.

مشغول is the masculine singular form.
مشغولة is the feminine singular form.

So:

• أنا مشغول = said by a male speaker
• أنا مشغولة = said by a female speaker
• صديقتي مشغولة = feminine, because صديقتي refers to a female friend

This is a very common pattern in Arabic.

Because here they are predicates, not adjectives directly attached to a noun.

Compare these two ideas:

صديقتي مشغولة = My friend is busy Here مشغولة is the predicate of the sentence.

صديقتي المشغولة = my busy friend Here المشغولة is an adjective modifying صديقتي inside a noun phrase.

So in your sentence, مشغول / مشغولة do not take الـ just because العمل and الجامعة are definite.

Because the word is صديقة and when you add the suffix ـي for my, the final ة changes in writing to ت.

So: صديقة = a female friend
صديقتي = my female friend

This happens regularly with words ending in ة:

• سيارة = car
• سيارتي = my car

So صديقتي is the normal and correct form.

It can mean either, depending on context.

Literally, صديقتي means my female friend. In some contexts, it can also mean my girlfriend.

So the word itself can be ambiguous. Usually the surrounding context tells you which meaning is intended.

في basically means in, but in many contexts it is best translated more naturally as at.

So:

• في العمل = at work
• في الجامعة = at the university / at university

Arabic often uses في where English prefers at for places or institutions.

You may also sometimes hear expressions like مشغول بالعمل, which means more like busy with work. That focuses more on what is causing the busyness, while مشغول في العمل focuses more on being busy at the place or in the setting of work.

Arabic often uses the definite article الـ in places where English may or may not use the.

So:

• في العمل is the normal way to say at work
• في الجامعة can mean at the university or simply at university, depending on context

In other words, the definite article in Arabic does not always match English word-for-word. It is often part of the natural idiom.

Because normal Arabic writing usually leaves them out.

So the sentence is written in the common unvocalized way: اليوم أنا مشغول في العمل، وصديقتي مشغولة في الجامعة.

If fully vocalized, it could be written like this: اليومَ أنا مشغولٌ في العملِ، وصديقتي مشغولةٌ في الجامعةِ.

Learners often notice that Arabic textbooks show more vowels than real-world writing. That is normal. Most everyday Arabic text does not write them, and readers understand from context.