The Civil war had an alternative , the ameable divorce that Chechoslovachia performed. The very hard Civil war had an alternative too the endless- neither side has enough to really win- civil war that Yugoslavia is not quite through with yet.
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There were no slaves involved in either part of Czechoslovakia. Both nations joined the EU and property rights of Czechs and Slovaks were respected. The US Civil War was not an ethnic struggle like those of the European nations. Slovakia is rural, poorer and more Slavic. The Czech Republic is industrial, more prosperous and more like Germany culturally. The Czechs got tired of subsidizing the Slovaks. The Slovaks were outvoted by the Czechs and got tired of Czech domination. Both sides gained by the separation. Miami has a Czechoslovakian Club, and they have not seen any reason to divide, as nearly all of them are Czechs.
Brazil abolished slavery in the 1890's, and became a Republic at the same time. There was a gradual end: they first declared that no one would be born a slave after a specified date, and then abolished it for older people about 20 years afterward. At that time, the older slaves' value had declined due to their age. Something similar happened in Cuba and the rest of the Spanish Empire.
This was not done in the US, mostly because the Southern Plantation slaveholders were such dogmatic assholes. This is easy to see by reading the literature of the time. The general tone was that the Plantation owners were actually protectors of the childlike slaves, and that slavery was GOOD for the poor darkies. Frederick Douglass and other literate Blacks were generally seen as exceptional, because they had some White blood.