From the division result above,
The quotient is
[tex]2x^2-x+3[/tex]While the remainder is 2
The result of the division can be written in the form
[tex](2x^2-x+3)\text{ +}\frac{2}{x-6}[/tex]The answer is
[tex]\frac{2x^3-13x^2+9x-16}{x-6}=\text{ }(2x^2-x+3)\text{ +}\frac{2}{x-6}[/tex]