\(\left(x^3-2x^x+3x-6\right):\left(x-2\right)\)
\(=x^3:\left(x-2\right)-2x^x:\left(x-2\right)+3x:\left(x-2\right)-6:\left(x-2\right)\)
\(=x^3:x-x^3:2-2x^x:x+2x^x:2+3x:x-3x:2-6:x+6:2\)
\(=x^2-\dfrac{x^3}{2}-2x^{x-1}+x^x+3-\dfrac{3x}{2}-\dfrac{6}{x}+3\)
\(=x^2-\dfrac{x^3+3x}{2}-2x^{x-1}+x^x+6-\dfrac{6}{x}\)