Answer
$\displaystyle \frac{x^{3}-x^{2}-2x+3}{x^{2}-3x+2}$
Work Step by Step
Adding fractions: we need a common denominator:
$(x-2)(x-1)$
$...=\displaystyle \frac{(x^{2}-1)(x-1)-1(x-2)}{(x-2)(x-1)}$
Numerator, first term, FOIL, second term: minus(...)
Denominator : FOIL
$=\displaystyle \frac{x^{3}-x^{2}-x+1-x+2}{x^{2}-x-2x+2}$
add like terms ...
$=\displaystyle \frac{x^{3}-x^{2}-2x+3}{x^{2}-3x+2}$
