Answer:
[tex]2x^2+1-\dfrac{x}{2x^2-3}[/tex]
Step-by-step explanation:
Use the long division method to divide polynomials:
[tex]\large \begin{array}{r}2x^2\phantom{)))))}+1\phantom{)}\\2x^2-3{\overline{\smash{\big)}\,4x^4-4x^2-x-3\phantom{)}}}\\\underline{-~\phantom{(}(4x^4-6x^2)\phantom{-b))))))}}\\0+2x^2-x-3\phantom{)}\\\underline{-~\phantom{()}(2x^2\phantom{))))}-3)}\\-x\phantom{))))))}\end{array}[/tex]
Therefore:
[tex]\dfrac{4x^4-4x^2-x-3}{2x^2-3}=2x^2+1-\dfrac{x}{2x^2-3}[/tex]
