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Assumptions in sage


I am a sage beginner and I wish to know that How sage handles assumptions ?

My example is as follows.

a= var('a'); solve((a-1)*x ==3, x);

and sage solves and gives correct solution [x==(3 / (a - 1))]. But here how the assumption (a != 1) is handled ? Because solution is not defined for (a=1).

Best regards