Answer with explanation:
[tex]\frac{(x^3 - 3x^2 + 5 x - 3)}{x -1}\\\\=\frac{x^3-x^2-2x^2+2 x +3 x -3}{x-1}\\\\ =\frac{x^2\times(x-1)-2 x \times (x-1)+3 \times (x-1)}{x-1}\\\\ \text{Taking,(x-1) common from three distinct terms in numerator} \\\\=\frac{(x-1)(x^2 -2 x +3)}{x-1}\\\\\text{Cancelling ,(x-1) from numerator and denominator}\\\\ \text{Quotient}=x^2 -2 x +3[/tex]
