1: \(\dfrac{6x^2-3x+5}{2x-1}\)
\(=\dfrac{3x\left(2x-1\right)+5}{2x-1}=3x+\dfrac{5}{2x-1}\)
2: \(\dfrac{x^3-11x^2+27x-9}{x-3}\)
\(=\dfrac{x^3-3x^2-8x^2+24x+3x-9}{x-3}\)
\(=\dfrac{x^2\left(x-3\right)}{x-3}-\dfrac{8x\left(x-3\right)}{x-3}+\dfrac{3\left(x-3\right)}{x-3}\)
\(=x^2-8x+3\)
3: \(\dfrac{x^3-3x^2-9x-5}{x-5}\)
\(=\dfrac{x^3-5x^2+2x^2-10x+x-5}{x-5}\)
\(=\dfrac{x^2\left(x-5\right)+2x\left(x-5\right)+\left(x-5\right)}{x-5}=x^2+2x+1\)
4: \(\dfrac{-12x^3+6x^2+7x-1}{x-1}\)
\(=\dfrac{-12x^3+12x^2-6x^2+6x+x-1}{x-1}\)
\(=\dfrac{-12x^2\left(x-1\right)-6x\left(x-1\right)+\left(x-1\right)}{x-1}=-12x^2-6x+1\)
5: \(\dfrac{2x^3-4x^2+7x-39}{x-3}\)
\(=\dfrac{2x^3-6x^2+2x^2-6x+13x-39}{x-3}\)
\(=2x^2+2x+13\)
6: \(\dfrac{3x^3-3x^2+6x-24}{x-2}\)
\(=\dfrac{3x^3-6x^2+3x^2-6x+12x-24}{x-2}\)
\(=\dfrac{3x^2\cdot\left(x-2\right)+3x\left(x-2\right)+12\left(x-2\right)}{x-2}\)
\(=3x^2+3x+12\)
