Đáp án:
$\displaystyle x^{2} -2x+3$
Giải thích các bước giải:
$\displaystyle \begin{array}{{>{\displaystyle}l}} \left( x^{4} -4x^{2} +12x-9\right) :\left( x^{2} +2x-3\right)\\ =\frac{x^{4} -x^{3} +x^{3} -x^{2} -3x^{2} +3x+9x-9}{x^{2} -x+3x-3}\\ =\frac{x^{3}( x-1) +x^{2}( x-1) -3x( x-1) +9( x-1)}{x( x-1) +3( x-1)}\\ =\frac{\left( x^{3} +x^{2} -3x+9\right)( x-1)}{( x+3)( x-1)}\\ =\frac{\left( x^{3} +3x^{2} -2x^{2} -6x+3x+9\right)}{( x+3)}\\ =\frac{x^{2}( x+3) -2x( x+3) +3( x+3)}{x+3}\\ =\frac{\left( x^{2} -2x+3\right)( x+3)}{x+3} =x^{2} -2x+3 \end{array}$
