Which is correct?
I've got an acting job. Like you believe that.
I've got an acting job. Like you'd believe that.
I mean, what's the difference between these two sentences?
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Is that also from the "Friends" series?
If so, which statement appeared in the series?
It sounds as if the speaker is expressing their fear that what they said would not be believed.
You could add some words to make it more understandable:
"I said that like (as if) you would believe it, but you may not."
The "would" expresses expectation or uncertainty. The statement makes more sense with "would".
You might get a better answer if you provide more context and a video link.
There are some idiomatic phrases such as like you'd know!/like he'd ask! (where 'd stands for would). There is also the phrase like I care!, which does not contain would. These phrases are informal and are
used to emphasize that something that has been suggested is not true or would never happen
- They were asking me what I'd do if I won. Like that would ever happen! (Cambridge)
So in your second sentence, the speaker is pretty sure the person they are speaking to will (would) never believe what they just said.