THX, AnxiousLlama !!!
I think that the first one isn't 4 separate problems.....I think it's supposed to be
(x^2 + 4x + 3) / (2x - 1)
____________________
(x^2 + x) / (2x^2 - 3x + 1)
This can be expressed as
(x^2 + 4x + 3) (2x^2 - 3x + 1)
___________ x ______________ factor where possible
(2x - 1) ( x^2 + x )
(x + 3) ( x + 1) (2x - 1) ( x - 1)
___________ x _____________ "cancelling" we get
2x - 1 x ( x + 1)
(x + 3) ( x - 1) x^2 + 2x - 3
_____________ = ___________
x x