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I'm Polish-Canadian, living in Canada. I'm planning to travel to Australia for 6 weeks and I'm about to apply for a visitor visa. I found out holders of Polish passports are not required to pay the visa fee. Here is my question: I need to enter the US using my Canadian passport, as I don't have a visa on the Polish one. Then I'm planning to use my Polish passport to enter Australia. I have no idea which passport to show when leaving the USA.
If I show the Canadian one, they will ask for the Australian visa. If I show my Polish one they will ask me how I got in, since there is no record of me arriving into the USA. Do you have any clues what I should do?