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I got:

Domain of f is all x not equal to 1 or -3. The range is all real numbers.

x/(x-1)(x+3)

Domain of g is all x not equal to 1, but it can't be equal to -3 either because of f (this is the part I am not really sure about). The range is all real numbers.

x(x+3)/(x-1)

Yes, the domains are the same (Right?)