Chapter 6 - Section 6.4 - Dividing Polynomials: Long Division and Synthetic Division - Exercise Set - Page 371: 85

$\dfrac{3}{2}x^3+\dfrac{1}{4}x^2+\dfrac{1}{8}x-\dfrac{7}{16}+\dfrac{1}{16(2x-1)}$

Using the long division below, then \begin{array}{l}\require{cancel}\left( 3x^4-x-x^3+\dfrac{1}{2} \right)\div( 2x-1 )\\\\= \dfrac{3}{2}x^3+\dfrac{1}{4}x^2+\dfrac{1}{8}x-\dfrac{7}{16}+\dfrac{1}{16(2x-1)} .\end{array}