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I have a question and I hope you can help me. I've been learning English for many years but I'm still struggling with the difference between simple past and present perfect.

For example this sentence here:

"By the time I got to the office, the meeting (begin, already) had already begun without me. My boss (be) was furious with me and I (be) was fired."

Can I also say "My boss was furious with me and I have been fired."?

I lately read an article in the business insider with the topic "What to do right after you've been fired?". Could I say "What to do right after you got fired?" too?

My native language is German and for me both sounds perfectly fine when I just don't seem to get the difference. Are both sentences right and if so what exactly is the difference?

Help would be very much appreciated.

Thank you!

If the speaker were talking to someone soon after the firing, the "was...have been" construction would be appropriate.

The "have been" verb is in the present perfect progressive tense, which describes an action that began in the past and continues in the present, and may continue in the future. The speaker has been fired, so that is almost certainly going to continue!

This usage is right in the recent-firing case because the status of being fired and accepting it is still on the speaker's mind as being processed but isn't over yet.

"Was fired" is a usage that says, yes, the person got fired at that past point, and they've processed that and have moved on.

Compare "I have been dumped by my paramour" (still dealing with it) and "I was dumped" (that's in my past now and I've handled it).

The first thing to realise is that in most cases, whether or not to use the present perfect is a free choice: it depends on how you are choosing to relate the events to the present circumstances.

If you choose to use the perfect, you are expressing that the event which happened had some relevance to the present time. What that relevance is depends on many things: it might be that the event was very recent; it might be that it created a state which is still continuing; it might be that it is seen as part of a series of events which are still continuing; it might be that it has consequences now.

In this case, if you choose the present perfect, you are saying that being fired is relevant to the present: probably that you are in the state of having been fired, as Davo says. In this case "my boss was angry with me and I've been fired" probably means that this is very recent - today or maybe yesterday. If it was longer ago, I would have expected "and I was fired". But not necessarily: if you are choosing to emphasise the fact that you are still feeling the consequences of the firing, you might choose "I have been fired" even if it was much longer ago.

Can I also say "My boss was furious with me and I have been fired."?

That's an error, but it's not a grammatical error, more of a style error. "My boss was furious" is simple past. "I have been fired" is present perfect. Present perfect is a mixture of past and present; it discusses things that happened in the past, but does so with respect to the current situation. "I have been fired" means "My current state is fired". While the firing happened in the past, the focus is on the current state of unemployment. Thus, this breaks up the connection between the two clauses. "My boss was furious with me and I was fired" presents the two clauses as two connected facts: my boss was furious -> my firing resulted. "My boss was furious with me and I have been fired" breaks up the flow and makes these sound like two random facts you've decided to put in one sentence, rather than causally related.

Could I say "What to do right after you go fired?" too?

No, "go" can't be used that way. You can say "What to do right after you get fired?" or "What to do right after you are fired?"

You might want to post this on the German SE to get the perspective of people fluent in both languages as to how they compare.

Both are fine.

...and I was fired.

This explains what happened in the past - you were fired.

...and I have been fired.

This explains your current situation - you are in a state of having been fired.

Your sentence is set in the past "By the time I got to the office...". That is why the past tense is used, I think. There is also a sequence of events:
1.the meeting began 2.you got there late 3.boss was furious 4.you got fired. Past simple is also used for sequence in the past.

"I have been fired" could be used to announce this recent fact (announcement of news) which is on your mind now because it affects the present = you have to look for a new job.

"when you have been fired" is a passive sentence. Someone else has fired you, you have been fired by your boss.