a: \(\dfrac{6x^4-4x^2+3x-2}{3x-2}\)
\(=\dfrac{2x^2\left(3x-2\right)+\left(3x-2\right)}{3x-2}\)
\(=2x^2+1\)
b: \(\dfrac{6x^3+3x^2+4x+2}{3x^2+2}\)
\(=\dfrac{\left(6x^3+4x\right)+\left(3x^2+2\right)}{3x^2+2}\)
\(=\dfrac{2x\left(3x^2+2\right)+\left(3x^2+2\right)}{3x^2+2}=2x+1\)
c: \(\dfrac{x^5+4x^3+3x^2-5x+15}{x^3-x+3}\)
\(=\dfrac{x^5-x^3+3x^2+5x^3-5x+15}{x^3-x+3}\)
\(=\dfrac{x^2\left(x^3-x+3\right)+5\left(x^3-x+3\right)}{x^3-x+3}=x^2+5\)
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