ANSWER
[tex]\frac{3 {x}^{2} - 2x + 1 } {x - 1 } = 3x + 1 + \frac{2}{x - 1} [/tex]
EXPLANATION
The given function is
[tex] \frac{3 {x}^{2} - 2x + 1 } {x - 1 } [/tex]
The synthetic division is shown in the attachment.
The Remainnder is 2.
The quotient is
[tex]3x + 1[/tex]
Therefore
[tex]\frac{3 {x}^{2} - 2x + 1 } {x - 1 } = 3x + 1 +\frac{2}{x - 1} [/tex]