Question 941510
First we factor {{{x^3-2x^2+3x-6}}} by grouping



{{{x^3-2x^2+3x-6}}}



{{{(x^3-2x^2)+(3x-6)}}}



{{{x^2(x-2)+(3x-6)}}}



{{{x^2(x-2)+3(x-2)}}}



{{{(x^2+3)(x-2)}}}



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So {{{x^3-2x^2+3x-6}}} factors to {{{(x^2+3)(x-2)}}}



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We then use this factorization to help simplify



{{{(x^3-2x^2+3x-6)/(x-2)}}}



{{{((x^2+3)(x-2))/(x-2)}}}



{{{((x^2+3)highlight((x-2)))/(highlight((x-2)))}}}



{{{((x^2+3)cross((x-2)))/(cross((x-2)))}}}



{{{x^2+3}}}



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Therefore, {{{(x^3-2x^2+3x-6)/(x-2)}}} simplifies to {{{x^2+3}}}