To answer this question we will use long division.
Then:
[tex]\begin{gathered} Quotient=-2x, \\ Remainder=-3x+4. \end{gathered}[/tex]Therefore:
[tex]\frac{-6x^3+7x+4}{3x^2-5}=-2x+\frac{-3x+4}{3x^2-5}.[/tex]Answer:
[tex]\frac{-6x^3+7x+4}{3x^2-5}=-2x+\frac{-3x+4}{3x^2-5}.[/tex]