\(=\dfrac{3x^4-8x^3-10x^2+8x-5}{-2x^2+3x+1}\)
\(=\dfrac{-1}{2}\left(\dfrac{6x^4-16x^3-20x^2+16x-10}{2x^2-3x-1}\right)\)
\(=\dfrac{-1}{2}\left(\dfrac{6x^4-9x^3-3x^2-7x^3+10.5x^2+3.5x-27.5x^2+41.25x+13.75-28.75x-23.75}{2x^2-3x-1}\right)\)
\(=\dfrac{-1}{2}\left(3x^2-3.5x-13.75+\dfrac{-28.75x-23.75}{2x^2-3x-1}\right)\)