+129852 [ x^2 + 4x + 3 ] / [ 2x - 1 ]
_____________________ = [ invert the bottom fraction and multiply ]
[ x^2 + x ] / [ 2x^2 -3x + 1 ]
[ (x + 1) (x + 3) / [2x -1 ] * [ 2x^2 - 3x + 1 ] / [x^2 + x] =
(x + 1) ( x+ 3) / ( 2x - 1) * [ (2x -1) (x -1)] / [ x ( x + 1) ] =
(x + 1) ( x + 3) / [ x ( x + 1) ] * [ (2x - 1) (x - 1) ] / (2x -1) =
(x + 3) / x * (x - 1) =
(x + 3) (x -1) / x
