Question

How do you divide `(x^2 + 2x + 3)/(x-1)`?

Answer 1

As an alternative to the previous answer (since for me, at least it isn't clear how the initial line factors were derived)
you could try polynomial long division or synthetic division.

Explanation:

Polynomial long division for `(x^2+2x+3) div (x-1)` would look something like:
#{: (,,x,+3,), (,,"-----","-----","-----"), (x-1,")",x^2,+2x,+3), (,,x^2,-x,), (,,"-----","-----",), (,,,3x,+3), (,,,3x,-3), (,,,"-----","-----"), (,,,,6) :}#